31 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 How to cite this article: El Msiyah, C., & Madkour, J. (2022). Dynamics of the Moroccan industry indices network before and during the covid-19 pandemic. International Journal of Banking and Finance, 18(1), 31-50. https://doi. org/10.32890/ ijbf2023.18.1.2 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC 1Cherif El Msiyah & 2Jaouad Madkour 1National School of Commerce and Management Moulay Ismail University, Morocco 2 Faculty of Law and Economics Abdelmalek Essaadi University, Morocco 1Corresponding author: c.elmsiyah@umi.ac.ma Received: 28/7/2021 Revised: 18/10/2021 Accepted: 21/10/2021 Published: 5/1/2023 ABSTRACT This paper studies the topological properties of the dynamics of the industry indices network at the Moroccan stock exchange by using network theory. The Minimum Spanning Tree (MST) was constructed from the metric distances which had been calculated for the different pairs of industrial indices. The dynamics of the MST were analysed over the period 2013 to 2020 using the sliding window technique. The period studied was divided into the pre-pandemic Covid-19 period and the pandemic Covid-19 period. Connectivity and centrality indicators were calculated to track the connectivity structure over time and to identify the positioning and the importance of the industry indices studied. The result of this study indicates that the network of industry indices was relatively stable during the pre-pandemic Covid-19 period https://e-journal.uum.edu.my/index.php/ijbf INTERNATIONAL JOURNAL OF BANKING AND FINANCE 32 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 before observing a sudden rapprochement between industries when the Covid-19 pandemic was officially announced. The formation of star-shaped networks was also observed. These networks were centred on the banking industry, essentially during the pandemic Covid-19 period. The banking industry was also positioned at the centre of the Moroccan industry indices network. Keywords: Industry indices network, minimum spanning tree, covid-19, network connectivity, network centrality. JEL Classification: C45, G01, G11, G23. INTRODUCTION The use of network theory to translate the financial taxonomy of stock markets has been adopted by many research studies. In addition to some seminal works (Mantegna, 1999; Bonanno et al., 2000; Bonanno et al., 2001; Onnela et al., 2003), a large body of the literature has confirmed that stock markets behave like complex network systems; and it is possible to study the topological properties of financial networks, which have an associated significant economic taxonomy (Tabak et al., 2010). For Arthur et al. (1997), financial markets can be characterized as complex evolving systems, therefore it is useful to use the tools of complex network systems to analyse the stock market dynamics. According to De Carvalho and Gupta (2018), the network representation of stock market asset returns not only retains the most essential and important features of a large set of asset return co-movements, but also helps to simplify the challenges for identifying the co-movement dynamics between assets, including those related to the number of assets and risk factors that must be assessed simultaneously and the non-stationarity of movement in the asset dynamics. As the main tools of complex network theory, the clustering and filtering algorithms of the minimum spanning tree (MST) technique have been used to study the different topological and structural aspects of the stock markets, and also to illustrate their ability to transmit and exploit significant economic information. For example, Tumminello et al (2010) demonstrated the formation of clusters at different levels of trees and the possibility to define the taxonomy of stocks within 33 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 the network by applying the different procedures for grouping and for filtering the correlation matrix of daily returns. Tola et al. (2008) used clustering algorithms to improve the reliability of portfolios in terms of the ratio of the expected risk to the realised risk. They showed that clustering portfolio optimization methods often outperforms the Markowitz or random matrix theory methods. Khashanah and Miao (2011) applied the MST to the entire financial system, consisting of typical markets (stocks, bonds, derivatives, currencies, and commodities) to study the changes in the structure of the financial system during the economic downturn. With regard to the application of MST techniques on the stock market, a great deal of work has been done in both developed and emerging countries. For example, there has been work on certain emerging markets; Galazka (2011) used the MST to identify the stocks that strongly influenced the price dynamics of other stocks on the same Polish stock market, using a portfolio of 252 stocks in 2007. Majapa and Gossel (2016) applied the MST approach to study the topological evolution before, during and after the 2008-2009 crisis, by constructing a network map of the top 100 companies listed on the Johannesburg Stock Exchange. Sinha and Pan (2007) used data from 201 stocks over the period 1996–2006 to assess the strength of dominance of the largest companies in the Indian economy. Tabak et al. (2010) constructed the MST by using the weekly prices of the 47 stocks on the Brazilian stock exchange from January 7, 2000 to February 29, 2008, and by the correlation matrix for a variety of stocks of different industry indices. Moreover, the study showed that stocks tended to cluster by industry. Situngkir and Surya (2005) found that the Indonesian stock market became stable during the period from 2000 to 2004, just after the economic shock of the currency crisis. They also noted the dominance of several stocks in certain industries. The world has already faced health crises (SARS, MERS and Ebola, among others) that impacted the stock markets and business activities, but less forcefully than the Covid-19 pandemic (Baker et al., 2020). Ashraf (2020) used the daily Covid-19 confirmed cases and death cases, as well as the stock markets returns data from 64 countries and found that stock markets quickly reacted to the Covid-19 pandemic. Liu et al. (2020) found that Asia experienced the most negative abnormal returns among the 21 leading stock market indices in most affected countries. Haroon and Rizvi (2020) found that the overwhelming panic 34 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 generated by the news outlets has led to the increase in the volatility in the equity markets. Zhang et al. (2020) found that Covid-19 has led to an increase in the global financial market risk Aslam et al. (2020) examined the effects of Covid-19 on 56 global stock indices by using a complex network method and they revealed a structural change in the form of node changes, a reduced connectivity and significant differences in the topological characteristics of the network. As in Yang et al. (2014), the present study aims to apply the MST technique directly to industry indices in order to analyse the structural change of the stock market and to identify the key sectors of the Moroccan economy. The study of the dynamic evolution of the industry indices network will then allow one to see the impact of the crisis on the industrial structure of the stock market. In the second section, of this paper, the MST model is presented and its usefulness shown in terms of simplifying the dependency structure between nodes. The next section presents the details of the study data and their uses for the construction of MSTs of the Moroccan industry indices. In the fourth section, the discussion will turn to the use of some indicators to analyse the dynamics of MSTs. The last section will present the results and draw the relevant conclusions. METHODOLOGY Minimum Spanning Tree Model The use of the MST to translate the financial taxonomy consists in studying the financial assets connections through the evolution of their stock prices. In the context of the present study, the focus is on the industrial taxonomy of the Moroccan stock market. In this regard, the daily returns of the industry indices were used to calculate the correlation and distance matrix and to trace the MST for the Moroccan stock industries. Let be the number of industry indices studied. For an industry the rate of return on day is: is the closing price of on day 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 35 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 The Pearson correlation coefficient between two industries and : For an industry represents the average of the log-returns over the period studied. For trading days studied . The correlation coefficients calculated for each pair of industry indices and form a symmetric correlation matrix of dimension and in which its diagonal elements equal to unity. In total, the correlation matrix contains correlation coefficients fulfilling the condition . The correlation coefficient of a pair of industry indices cannot be used as the distance between the two industries and because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of the industry indices network, a variable is needed that can function as distance, satisfying the three axioms of Euclidean distance: The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007), and it is permitted to relate the distance of two variables (i.e. industry indices) to their correlation coefficients, as in Equation (1): (1) The correlation coefficients are therefore, used to calculate the distances and to construct a matrix of the distances of the industry indices of the same dimension as the correlation matrix .The small distances in the matrix imply the high correlations between industry indices. From the distance matrix, it can be seen that there is a directionless and fully connected graph in which the nodes are industry indices and the links between them are measured by the distances The MST is then constructed by using direct links between the nodes of ,such that the sum of the distances of these 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 36 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 links is minimal. In this way, the MST is constructed progressively by linking all the nodes together with the smallest distances. It can be started by linking the two closest (most correlated) nodes, the next node is added to the MST, with the condition that the added distance must be the smallest and also the addition of that node should not close the loop with the nodes that are already added to the MST. Kruskal’s algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal’s algorithm is presented in Yang et al. (2014). The number of links between nodes is considerably reduced by using the minimum spanning tree (MST). The present study therefore, will go from the d distances in the distance matrix to only ,the shortest distances in the MST. Data The data for the study were the prices of industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1,945 trading days As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014), and for analysis and smoothing purposes, the data were divided into windows of width The step between two consecutive windows was set at trading days The choice of was motivated by the fact that the period of the Covid-19 pandemic studied was 185 days (between March 01, 2020 to November 30, 2020); this period corresponded roughly to the time between the official announcement of the pandemic and the announcement of the vaccine availability. The step of corresponded roughly to the average number of trading days per month. Thus, this distribution of data consisted of studying the evolution of 89 MSTs, each corresponding to a window of 185 stock market prices with a 20-day shift (overlap) from one window to another. The last window studied corresponded to the entire period of the Covid-19 pandemic (March 01, 2020 to November 30, 2020). This choice was arbitrary with the fact that the choice of window width had been a compromise between too noisy and too smoothed data for small and large window widths, respectively (Onnela et al., 2003). Similarly, for the overlap step, the choice of very small might cause concerns related to its inability to identify the episodic changes in the networks because the network 1 DYNAMICS OF THE MOROCCAN INDUSTRY INDICES NETWORK BEFORE AND DURING THE COVID-19 PANDEMIC Minimum Spanning Tree (MST) model Let 𝑁𝑁𝑁𝑁 be the number of industry indices studied. For an industry 𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖 = 1, . . . , 𝑁𝑁𝑁𝑁), the rate of return on day 𝑡𝑡𝑡𝑡 is: 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡−1) � 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) is the closing price of 𝑖𝑖𝑖𝑖 on day 𝑡𝑡𝑡𝑡 . The Pearson correlation coefficient between two industries 𝑖𝑖𝑖𝑖 and 𝑗𝑗𝑗𝑗: 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥������−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� ��𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤 2����−𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤��� 2��𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥 2����−𝑅𝑅𝑅𝑅𝚥𝚥𝚥𝚥��� 2� For an industry 𝑖𝑖𝑖𝑖 , 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� represents the average of the log-returns 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) over the period studied. For 𝑇𝑇𝑇𝑇 trading days studied, 𝑅𝑅𝑅𝑅𝚤𝚤𝚤𝚤� = 1 𝑇𝑇𝑇𝑇 ∑ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡=1 . 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝑡𝑡𝑡𝑡 of 𝑁𝑁𝑁𝑁 × 𝑁𝑁𝑁𝑁 𝑁𝑁𝑁𝑁(𝑁𝑁𝑁𝑁 − 1)/2 1 ≤ 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 1 � 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖𝑖𝑖 = 𝑗𝑗𝑗𝑗 (positive definiteness) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖+𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (triangle inequality) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = �2�1 − 𝜌𝜌𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖� (1) 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖𝑖𝑖)∈MST The 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 4 of the pandemic and the announcement of the vaccine. The step of 𝑑𝑑𝑑𝑑 = 20 roughly corresponds to the average number of trading days per month. Thus, this distribution of data consists of studying the evolution of 89 MSTs each corresponding to a window of 185 stock market prices with a 20-day shift (overlap) from one window to another. The last window studied corresponds to the entire period of the Covid-19 pandemic (March 01, 2020 to November 30, 2020). This choice remains arbitrary in view of the fact that the choice of window width is a compromise between too noisy and too smoothed data for small and large window widths respectively (Onnela et al., 2003). Similarly for the overlap step, the choice of very small dW may raise concerns about the inability to identify episodic changes in the networks as the network carries a large proportion of the observations between successive windows (De Carvalho & Gupta, 2018). The MSTs constructed for different time windows are not independent of each other (two successive MSTs share 165 trading days over an analyzed MST period of 185 trading days), but form a series over time. Therefore, this multitude of trees is interpreted as a sequence of evolutionary steps of a single dynamic asset tree (Onnela et al., 2003) The 21 stock market industry indices studied are classified as in Table 1. The MSTs corresponding to the two periods, the pre-pandemic period (January 23, 2013 to February 29, 2020) and the pandemic period (March 1, 2020 to April 30, 2020) are given in Figure 1. Table 1 Industry indices included in the study and their tickers. Notes: index and ticker symbol are given by the authors and the industry indices correspond to that of the Casablanca Stock Exchange. Data Analysis A simple comparison of these two MSTs allows us to see that the industries are much more centered on the banking industry during the period of the covid-19 pandemic than during the period before the covid-19 pandemic. It is also pointed that the industries with which the banking industry is directly linked before the pandemic are also linked during the pandemic period; this is the case for “Real estate participation and development” industry (link 3-14), “Building and construction materials” industry (link 3-4), “Food/ production” industry (link 3-1) and “Telecommunication” industry (link 3- 20). This result is consistent with that of Musmeci et al. (2015) who, using filtered correlations between US stocks over the period from January 1997 to December 2012, lead to a pattern of clustering that changes radically with the outbreak of the financial crisis of 2007. The change in structure is analysed in more detail below using some connectivity and centrality indicators. 4 of the pandemic and the announcement of the vaccine. The step of 𝑑𝑑𝑑𝑑 = 20 roughly corresponds to the average number of trading days per month. Thus, this distribution of data consists of studying the evolution of 89 MSTs each corresponding to a window of 185 stock market prices with a 20-day shift (overlap) from one window to another. The last window studied corresponds to the entire period of the Covid-19 pandemic (March 01, 2020 to November 30, 2020). This choice remains arbitrary in view of the fact that the choice of window width is a compromise between too noisy and too smoothed data for small and large window widths respectively (Onnela et al., 2003). Similarly for the overlap step, the choice of very small dW may raise concerns about the inability to identify episodic changes in the networks as the network carries a large proportion of the observations between successive windows (De Carvalho & Gupta, 2018). The MSTs constructed for different time windows are not independent of each other (two successive MSTs share 165 trading days over an analyzed MST period of 185 trading days), but form a series over time. Therefore, this multitude of trees is interpreted as a sequence of evolutionary steps of a single dynamic asset tree (Onnela et al., 2003) The 21 stock market industry indices studied are classified as in Table 1. The MSTs corresponding to the two periods, the pre-pandemic period (January 23, 2013 to February 29, 2020) and the pandemic period (March 1, 2020 to April 30, 2020) are given in Figure 1. Table 1 Industry indices included in the study and their tickers. Notes: index and ticker symbol are given by the authors and the industry indices correspond to that of the Casablanca Stock Exchange. Data Analysis A simple comparison of these two MSTs allows us to see that the industries are much more centered on the banking industry during the period of the covid-19 pandemic than during the period before the covid-19 pandemic. It is also pointed that the industries with which the banking industry is directly linked before the pandemic are also linked during the pandemic period; this is the case for “Real estate participation and development” industry (link 3-14), “Building and construction materials” industry (link 3-4), “Food/ production” industry (link 3-1) and “Telecommunication” industry (link 3- 20). This result is consistent with that of Musmeci et al. (2015) who, using filtered correlations between US stocks over the period from January 1997 to December 2012, lead to a pattern of clustering that changes radically with the outbreak of the financial crisis of 2007. The change in structure is analysed in more detail below using some connectivity and centrality indicators. 37 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 carried a huge portion of the observations between the successive windows (De Carvalho & Gupta, 2018). The constructed MSTs for different time windows were not independent of each other (two successive MSTs share 165 trading days over an analyzed MST period of 185 trading days), but form a series over time. Therefore, this multitude of trees was interpreted as a sequence of evolutionary steps of a single dynamic asset tree (Onnela et al., 2003) The 21 stock market industry indices studied are classified as in Table 1. The MSTs corresponding to the two periods, the pre-pandemic period (January 23, 2013 to February 29, 2020) and the pandemic period (March 1, 2020 to April 30, 2020) are as given in Figure 1. Table 1 Industry Indices Included in the Study and their Tickers Index (1) ticker symbol (1) industry indice (1) index (2) ticker symbol (2) industry indice (1) 1 FP Food / production 12 H&SS Hardware, software and services 2 INSUR Insurance 13 MINES Mines 3 BANK Banks 14 RE Real estate participation and development 4 B&CM Building and construction materials 15 O&G Oil and gas 5 DRINK Drinks 16 UTIL Utilities 6 CHEM Chemistry 17 FC&OF Funding company and other financial activities 7 DISTR Distributors 18 PC&H Portfolio companies and Holding companies 8 EEE Electronic and electrical equipment 19 F&P Forestry and paper 9 PHARM Pharmaceutical industry 20 TCOM Telecommunication 10 EIE Engineering and industrial equipment 21 TRANS Transport 11 L&H Leisure and hotels Notes. Index and ticker symbols are given by the authors and the industry indices correspond to that of the Casablanca Stock Exchange. 38 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 Data Analysis A simple comparison of the two MSTs allows us to see that the industries were much more centred on the banking industry during the period of the covid-19 pandemic than during the period before the covid-19 pandemic. It should also bevpointed out that the industries linked directly to the banking industry before the pandemic were also linked during the pandemic period; this is the case for “Real estate participation and development” industry (link 3-14), “Building and construction materials” industry (link 3-4), “Food/ production” industry (link 3-1) and “Telecommunication” industry (link 3-20). This result is consistent with that of Musmeci et al. (2015) who, using filtered correlations between US stocks over the period from January 1997 to December 2012, showed a pattern of clustering that changes radically with the outbreak of the financial crisis of 2007. The change in structure is analysed in more detail below using some of the connectivity and centrality indicators. Figure 1 Minimum Spanning Trees (MST) of the Industry Indices of the Covid-19 Pandemic Period (b) and the Covid-19 Pre-pandemic Period (a) RESULTS AND ANALYSIS Network Connectivity Dynamics of Industry Indices In addition to the calculation of the overall distance of MSTs, the present study used some key indicators to identify the most important 6 RESULTS AND ANALYSIS Network Connectivity Dynamics of Industry Indices In addition to the calculation of the overall distance of MSTs, the present study used some key indicators to identify the most important connections between the industry indices, and to analyse their evolution over the period under review. For the 20 distances of the links belonging to MST, the size of MST is calculated by Equation (2): (2) For 89 MSTs generated between January 23, 2013 and November 30, 2020, the last 9 MSTs (MST 81 to MST 89) had part of the period covered (185 trading days) during the Covid-19 pandemic. Specifically, the 81st MST covered 160 days before the pandemic period (before March 1, 2020) and 25 trading days during the pandemic period (from March 1). The 82nd MST covered 140 days before the pandemic period and 45 trading days during the pandemic period and so on until the last MST (89th) which covered the pandemic period from March 1, 2020 to November 30, 2020. It can be seen that the MST size (MST-Distance) of the last 9 MSTs decreased on average from 25.03 before the pandemic period to 19.5 during the pandemic period. It was also noted that from the 81st MST and for only 25 covered trading days, there was practically the same level of decline. Indeed, the size of the 81st MST, which covered the period from September 21, 2019 to March 25, 2020, showed a comparable decline with the MSTs covering a larger fraction of the pandemic period. This can be explained by the brutal reaction of the stock market from the first days of the official announcement of the pandemic. For a given MST and a knowledge of N, i.e., the number of industry indices studied, the mean and the standard deviation of the link distances in MST is as expressed in Equation (3) and Equation (4): (3) (4) 39 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 connections between the industry indices, and to analyse their evolution over the period under review. For the 20 distances of the links belonging to MST, the size of MST is calculated by Equation (2): (2) For 89 MSTs generated between January 23, 2013 and November 30, 2020, the last 9 MSTs (MST 81 to MST 89) had part of the period covered (185 trading days) during the Covid-19 pandemic. Specifically, the 81st MST covered 160 days before the pandemic period (before March 1, 2020) and 25 trading days during the pandemic period (from March 1). The 82nd MST covered 140 days before the pandemic period and 45 trading days during the pandemic period and so on until the last MST (89th) which covered the pandemic period from March 1, 2020 to November 30, 2020. It can be seen that the MST size (MST-Distance) of the last 9 MSTs decreased on average from 25.03 before the pandemic period to 19.5 during the pandemic period. It was also noted that from the 81st MST and for only 25 covered trading days, there was practically the same level of decline. Indeed, the size of the 81st MST, which covered the period from September 21, 2019 to March 25, 2020, showed a comparable decline with the MSTs covering a larger fraction of the pandemic period. This can be explained by the brutal reaction of the stock market from the first days of the official announcement of the pandemic. For a given MST and a knowledge of N, i.e., the number of industry indices studied, the mean and the standard deviation of the link distances in MST is as expressed in Equation (3) and Equation (4): (3) (4) Where is the number of links in the MST. 2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑇𝑇𝑇𝑇 − 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (2) 𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (3) 𝜎𝜎𝜎𝜎𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ �𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑑𝑑𝑑𝑑� 2 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (4) 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 = 1 𝑁𝑁𝑁𝑁−1 × �𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡 ∩ 𝐸𝐸𝐸𝐸(𝑡𝑡𝑡𝑡−1)� (5) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖 = ∑ 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖=1 (6) 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) = 1 𝑁𝑁𝑁𝑁 ∑ ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖=1 (7) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝐵𝐵𝐵𝐵𝐶𝐶𝐶𝐶(𝑖𝑖𝑖𝑖) = ∑ 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗(𝑖𝑖𝑖𝑖) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗 𝑖𝑖𝑖𝑖≠𝑖𝑖𝑖𝑖 (8) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖) 5 Figure 1 Minimum Spanning Trees (MST) of the industry indices of the Covid-19 pandemic period (b) and the Covid-19 pre-pandemic period (a). RESULTS AND ANALYSIS Network connectivity dynamics of industry indices In in addition to the calculation of the overall distance of MSTs, we use some key indicators to identify the most important connections between the industry indices and analyse their evolution over the period under review. For the 20 distances 𝑑𝑑𝑖𝑖𝑖𝑖 of the links belonging to MST, the size of MST is calculated by: 𝑀𝑀𝑀𝑀𝑀𝑀 − 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑖𝑖𝑖𝑖𝑑𝑑𝑖𝑖𝑖𝑖∈MST (2) For 89 MSTs generated between January 23, 2013 and November 30, 2020, the last 9 MSTs (MST 81 to MST 89) have part of the period covered (185 trading days) during the Covid-19 pandemic. Specifically, the 81st MST covers 160 days before the pandemic period (before March 1, 2020) and 25 trading days during the pandemic period (from March 1). The 82nd MST covers 140 days before the pandemic period and 45 trading days during the pandemic period and so on until the last MST (89th) which covers exactly the pandemic period (March 1, 2020 - November 30, 2020). It can be seen that the MST size (MST-Distance) of the last 9 MSTs increases on average from 25.03 before the pandemic period to 19.5 for the MSTs corresponding to the pandemic period. We also note that from the 81st MST and for only 25 covered trading days, we have practically the same level of decline. This can be explained by the brutal reaction of the stock market from the first days of official announcement of the pandemic. 2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑇𝑇𝑇𝑇 − 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (2) 𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (3) 𝜎𝜎𝜎𝜎𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ �𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑑𝑑𝑑𝑑� 2 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (4) 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 = 1 𝑁𝑁𝑁𝑁−1 × �𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡 ∩ 𝐸𝐸𝐸𝐸(𝑡𝑡𝑡𝑡−1)� (5) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖 = ∑ 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖=1 (6) 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) = 1 𝑁𝑁𝑁𝑁 ∑ ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖=1 (7) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝐵𝐵𝐵𝐵𝐶𝐶𝐶𝐶(𝑖𝑖𝑖𝑖) = ∑ 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗(𝑖𝑖𝑖𝑖) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗 𝑖𝑖𝑖𝑖≠𝑖𝑖𝑖𝑖 (8) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖) 2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑇𝑇𝑇𝑇 − 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (2) 𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (3) 𝜎𝜎𝜎𝜎𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ �𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑑𝑑𝑑𝑑� 2 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (4) 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 = 1 𝑁𝑁𝑁𝑁−1 × �𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡 ∩ 𝐸𝐸𝐸𝐸(𝑡𝑡𝑡𝑡−1)� (5) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖 = ∑ 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖=1 (6) 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) = 1 𝑁𝑁𝑁𝑁 ∑ ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖=1 (7) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝐵𝐵𝐵𝐵𝐶𝐶𝐶𝐶(𝑖𝑖𝑖𝑖) = ∑ 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗(𝑖𝑖𝑖𝑖) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗 𝑖𝑖𝑖𝑖≠𝑖𝑖𝑖𝑖 (8) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖) 3 For an industry 𝑖𝑖 , 𝑅𝑅�̅�𝑖 represents the average of the log-returns 𝑅𝑅𝑖𝑖 (𝑡𝑡) over the period studied. For 𝑇𝑇 trading days studied, 𝑅𝑅�̅�𝑖 = 1 𝑇𝑇 ∑ 𝑅𝑅𝑖𝑖 (𝑡𝑡)𝑇𝑇𝑡𝑡=1 . The correlation coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 calculated for each pair of industry indices 𝑖𝑖 and 𝑗𝑗 form a symmetric correlation matrix 𝐶𝐶𝑡𝑡 of dimension 𝑁𝑁 × 𝑁𝑁 and whose diagonal elements equal to unity. In total, the correlation matrix contains 𝑁𝑁(𝑁𝑁 − 1)/2 correlation coefficients fulfilling the condition 1 ≤ 𝜌𝜌𝑖𝑖𝑖𝑖 ≤ 1. The correlation coefficient of a pair of industry indices 𝜌𝜌𝑖𝑖𝑖𝑖 cannot be used as the distance between the two industries 𝑖𝑖 and 𝑗𝑗 because it does not fulfill the three axioms that define a metric (Mantegna, 1999). Indeed, to analyse the topological taxonomy of our industry indices network, we need a variable that can function as distance, satisfying the three axioms of Euclidean distance: { 𝑑𝑑𝑖𝑖𝑖𝑖 = 0 if and only if 𝑖𝑖 = 𝑗𝑗 (positive definiteness) 𝑑𝑑𝑖𝑖𝑖𝑖 = 𝑑𝑑𝑖𝑖𝑖𝑖 (symmetry) 𝑑𝑑𝑖𝑖𝑖𝑖 ≤ 𝑑𝑑𝑖𝑖𝑖𝑖 +𝑑𝑑𝑖𝑖𝑖𝑖 (triangle inequality) The metric distance, introduced by Mantegna (1999), is determined from the Euclidean distance (Coelho et al., 2007) and makes it possible to relate the distance of two variables (i.e. industry indices) to their correlation coefficients: 𝑑𝑑𝑖𝑖𝑖𝑖 = √2(1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) (1) The correlation coefficients are therefore used to calculate the distances and to construct a matrix of the distances of the industry indices 𝐷𝐷𝑡𝑡 of the same dimension as the 𝑁𝑁 × 𝑁𝑁 correlation matrix. Small distances in the matrix imply high correlations between industry indices. From the distance matrix 𝐷𝐷𝑡𝑡, we can draw a directionless and fully connected graph 𝐺𝐺 in which the nodes are industry indices and the links between them are measured by the distances 𝑑𝑑𝑖𝑖𝑖𝑖 . The MST is then constructed using (𝑁𝑁 − 1) direct links between the 𝑁𝑁 nodes of 𝐺𝐺 such that the sum of the (𝑁𝑁 − 1) distances of these links ∑ 𝑑𝑑𝑖𝑖𝑖𝑖(𝑖𝑖,𝑖𝑖)∈MST is minimal. The MST is constructed in this way by progressively linking all the nodes together with the smallest distances; starting by linking the two closest (most correlated) nodes, the next node is added to the MST provided that the added distance is the smallest and that the addition of this node does not close the loop with the nodes already added to the MST. Kruskal's algorithm is used for this purpose. A detailed approach to constructing MSTs using Kruskal's algorithm is presented in (Yang et al., 2014). The number of links between nodes is considerably reduced by using minimum spanning tree (MST). We therefore go from 𝑁𝑁 × (𝑁𝑁 − 1)/2 distances in the distance matrix 𝐷𝐷𝑡𝑡 to only (𝑁𝑁 − 1) shortest distances in the MST. Data The data we will study concern the prices of 𝑁𝑁 = 21 industry indices of the Moroccan stock exchange from January 23, 2013 to November 30, 2020, i.e. a total of 1945 trading days 𝑡𝑡 = 1,2, . . . , 1945. As in Onnela et al. (2003), Tabak et al. (2010) and Yang et al. (2014) and for analysis and smoothing purposes, the data are divided into 𝑤𝑤 = 1.2 … .89 windows of width 𝑊𝑊 = 185 . The step between two consecutive windows is set at 20 trading days 𝑑𝑑𝑊𝑊 = 20 . The choice of 𝑊𝑊 = 185 is motivated by the fact that the period of the Covid-19 pandemic studied is 185 days (between March 01, 2020 to November 30, 2020); this period corresponds roughly to the time between the official announcement 40 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 Figure 2 Distance Mean (a) and Distance Standard Deviation (b) of MST Links The mean and standard deviation of the link distances in the MST are represented as a function of time for the different MSTs generated in Figure 2. The average distance of links in the MSTs decreased from 1.25 during the pre-pandemic period to 0.97 for MSTs in the pandemic period. This represents a decrease of about 22 percent from one period to the next, the industry indices were thus 22 percent closer on average during the pandemic period (indicating more correlation between indices). The decrease in the average distance of links is in line with the results of several studies, which have shown an increase in the mean correlation (decrease in average distance of links) during market crashes (see Onnela et al. (2003), Drozdz et al. (2000), and Majapa and Gossel (2016). The result is also partly consistent with that of Ang and Chen (2010) who, in studying the correlations between US equities and the overall US market, found that correlations increased following downside moves, particularly for extreme downside moves than for upside moves. This asymmetry of correlation movement was also demonstrated by Longin and Solnik (2001) who also found that correlations were higher during bear markets than in bull markets. The decrease in the average distance of links was accompanied by a very high variation in the distance standard deviation of links between the two periods (Figure 2b). The standard deviation increased from 0.057 on average during the pre-pandemic period to 0.204 during the 41 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 pandemic period (for a minimum of 0.63 and a maximum of 1.32); which was an increase of 255 per cent. According to Khashanah and Miao (2011), this clearly visible jump in the distance standard deviation could be explained by the intensification of systemic risk; correlations thus, appeared more uncertain due to unexpected and urgent responses to market events. As for the distance standard deviation of links, the variability was also remarkable. For the pre- pandemic period, the minimum distance was 1.13 and the maximum distance was 1.34, whereas during the pandemic period, the minimum distance was 0.63 and the maximum distance was 1.32. The combined effect was reflected in the strengthening of the links between industries (nodes), as can be seen in Figure 1b. This may occur either because of the strengthening of existing links in MST, as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from the MST. For a better visualization of the successive topological changes in MSTs and in particular, the links with the banking industry, the survival rate of direct links in MSTs were calculated (Onnela et al., 2003). In a single step, the simple survival rate calculates the percentage of links (between each 2 industry indices) that survive from one MST to another. For two consecutive MSTs at times and , the simple survival rate is given by Equation (5): (5) Where is the set of MST links at time, is the intersection operator and gives the number of elements in the set. In the short term, it can be said that the high level of simple survival rates reflected a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period) was noted. This was in comparison to the average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. Thus, one could conclude that the strengthening of the links between industries (nodes) in successive MSTs occurred, to a large extent, as a result of the strengthening of already existing links. 2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑇𝑇𝑇𝑇 − 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (2) 𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (3) 𝜎𝜎𝜎𝜎𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ �𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑑𝑑𝑑𝑑� 2 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (4) 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 = 1 𝑁𝑁𝑁𝑁−1 × �𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡 ∩ 𝐸𝐸𝐸𝐸(𝑡𝑡𝑡𝑡−1)� (5) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖 = ∑ 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖=1 (6) 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) = 1 𝑁𝑁𝑁𝑁 ∑ ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖=1 (7) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝐵𝐵𝐵𝐵𝐶𝐶𝐶𝐶(𝑖𝑖𝑖𝑖) = ∑ 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗(𝑖𝑖𝑖𝑖) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗 𝑖𝑖𝑖𝑖≠𝑖𝑖𝑖𝑖 (8) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖) 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 42 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 In both the pre- pandemic and pandemic periods, the banking industry was the most surviving node (see Figure 3). Figure 3 Number of Times the Nodes have Survived both during the Covide-19 Pandemic Period and before the Covide-19 Pandemic Period Figure 4 Number of Times the Nodes have Survived together with BANK node, both during the Covide-19 Pandemic Period and before the Covide-19 Pandemic Period During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 7 As for the distance standard deviation of links, the variability is also remarkable. For the pre- pandemic period, the minimum distance is 1.13 and the maximum distance is 1.34, whereas during the pandemic period, the minimum distance is 0.63 and the maximum distance is 1.32. The combined effect is reflected in the strengthening of the links between industries (nodes) as seen in Figure 1b. This may occur either because of the strengthening of existing links in MST as is the case for some industries whose linkage has become closer to the banking industry, or because weaker links (of high distance) are deactivated from MST. To better visualize successive topological changes in MSTs and in particular the links with the banking industry, we calculate the survival rate of direct links in MSTs (Onnela et al., 2003). In a single step, the simple survival rate is calculated for two consecutive MSTs at times 𝑡𝑡 and 𝑡𝑡 − 1 (𝑡𝑡 = 2, … , 89) by: 𝜎𝜎𝑡𝑡 = 1 𝑁𝑁−1 × |𝐸𝐸𝑡𝑡 ∩ 𝐸𝐸(𝑡𝑡−1)| (5) Where 𝐸𝐸𝑡𝑡 is the set of MST links at time 𝑡𝑡, ∩ is the intersection operator and | . . . | gives the number of elements in the set. Figure 3 Number of times the nodes have survived both during the Covide-19 pandemic period and before the Covide-19 pandemic period. In the short term, it can be said that the high level of simple survival rates reflects a certain topological stability in the configuration of the industry indices network. Indeed, compared to a total number of direct links (𝑁𝑁 − 1 = 20), we note an average survival rate of 67.56 per cent (13.51 links from one MST to another over the pre- pandemic period). This compares with an average survival rate of 80 per cent (16 links from one MST to another) during the pandemic period. It can be concluded from this that the strengthening of links between industries (nodes) in successive MSTs occurs, to a large extent, as a result of the strengthening of already existing links. In both the pre- pandemic and pandemic periods, the banking industry is the most surviving node (Figure 3). During the pre- pandemic period, the banking industry survived 197 times, of which 46 times with the “Telecommunication” node (link 3-4), 31 times with the “Building and construction materials” node (link 3-4), 29 times with the “Real estate participation and development” node (link 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 43 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 3-4), 29 times with the “Real estate participation and development” node (link 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (see Figure 4). Dynamic Analysis of Network Centrality In addition to the connectivity indicators discussed above, centrality indicators contained very useful additional information about the structure of the network topology. The node degree is the basic indicator for measuring the clustering and the centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For nodes of the MST, the degree of node is given by the Equation (6): (6) Where denotes the indicator function that gives in a condition that the node is directly linked to and otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (see Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. Table 2 Degrees of the Main Nodes BANK FP O&G B&CM RE January 23, 2013 to February 29, 2020 4 3 4 3 2 March 1, 2020 to November 30, 2020 12 3 1 1 2 Notes. Table 2 uses the tickers defined in Table 1 Dynamic monitoring of the time sequence of MSTs allows us to identify the central node for the 89 MSTs and the degree of centrality 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑇𝑇𝑇𝑇 − 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (2) 𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (3) 𝜎𝜎𝜎𝜎𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ �𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑑𝑑𝑑𝑑� 2 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (4) 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 = 1 𝑁𝑁𝑁𝑁−1 × �𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡 ∩ 𝐸𝐸𝐸𝐸(𝑡𝑡𝑡𝑡−1)� (5) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖 = ∑ 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖=1 (6) 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) = 1 𝑁𝑁𝑁𝑁 ∑ ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖=1 (7) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝐵𝐵𝐵𝐵𝐶𝐶𝐶𝐶(𝑖𝑖𝑖𝑖) = ∑ 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗(𝑖𝑖𝑖𝑖) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗 𝑖𝑖𝑖𝑖≠𝑖𝑖𝑖𝑖 (8) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖) 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 8 3-14). During the pandemic period (for the last 9 MSTs), the banking industry survived 77 times, including 8 times (out of the 8 MSTs) with 6 nodes including the nodes “Telecommunication”, “Building and construction materials” and “Real estate participation and development” (Figure 4). Figure 4 Number of times the nodes have survived with BANK both during the Covide-19 pandemic period and before the Covide-19 pandemic period. Dynamic analysis of network centrality In addition to the connectivity indicators discussed above, centrality indicators contain additional very useful information about the structure of the network topology. The node degree is the basic indicator for measuring clustering and centrality in a network, it is equal to the number of direct links connecting a given node to other nodes in the network. For 𝑁𝑁 nodes of MST, the degree of node 𝑗𝑗 is given by: 𝐷𝐷𝐷𝐷𝐷𝐷𝑗𝑗 = ∑ 𝐼𝐼𝑗𝑗𝑗𝑗𝑁𝑁𝑗𝑗=1 (6) Where 𝐼𝐼𝑗𝑗𝑗𝑗 denotes the indicator function that gives 1 if node 𝑗𝑗 is directly linked to 𝑘𝑘, and 0 otherwise. Table 2 summarizes the degrees of the main nodes over the entire pre- pandemic and the entire pandemic periods (Figure 1). It can be seen that the banking industry dominates the dynamics of the industry indices mainly during the pandemic period. The other industries have a lower weight in the network. The case of the “Oil and Gas” industry shows a disconnected evolution possibly due to the deep price drop. 44 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 of the different industries. From Gilmorea et al. (2008), the central node was defined as the node (industry) with the greatest number of direct links (the maximum degree of node). In the cases where the two nodes have the same number of direct links, the node with the lowest sum of distances of its links is selected. This is the same principle used in the construction of MSTs because the short connections link the node more closely to its neighbourhood than long connections (Onnela et al., 2003). Figure 5 MSTs Central Nodes During the whole period studied in Figure 5, the banking industry dominated the share of central nodes of MSTs (28.09 percent), followed by “Building and construction materials” industry and “Real estate participation and development” industry with shares equal to 11.236 per cent. These three industries together constituted 50 percent of the central nodes. During the pandemic period, the banking industry monopolized almost half of the direct links (9 to 12, out of 21) while the average for the pre- pandemic period was 4,737 direct links. Thus, the banking industry positioned itself as the central node for all MSTs during the pandemic period. The network connecting the BANK node during the pandemic period demonstrates the formation of a very star- like network structure (see Figure 1b) compared to the shape of the network before the pandemic period (see Figure 1a). The formation of star-shaped networks was directly related to a higher maximum node degree (De Carvalho & Gupta, 2018). 9 Table 2 Degrees of the main nodes. Notes: This table uses the tickers defined in Table 1. Dynamic monitoring of the time sequence of MSTs allows us to identify the central node for the 89 MSTs and the degree of centrality of the different industries. From Gilmorea et al. (2008), we define the central node as the node (industry) with the greatest number of direct links (the maximum degree of node). In cases where two nodes have the same number of direct links, the node with the lowest sum of distances of its links is selected. This is the same principle used in the construction of MSTs because short connections link the node more closely to its neighbourhood than long connections (Onnela et al., 2003). Figure 5 MSTs central nodes. During the whole period studied in Figure 5, the banking industry dominates the share of central nodes of MSTs with (28.09 per cent), followed by “Building and construction materials” industry and “Real estate participation and development” industry with shares equal to 11.236 per cent. These three industries together constitute 50 per cent of the central nodes. During the pandemic period, the banking industry monopolizes almost half of the direct links (9 to 12 out of 21) while the average for the pre- pandemic period is 4,737 direct links. The banking industry thus positions itself as the central node for all MSTs during the pandemic period. The degree tracking of the “BANK” node demonstrates the formation of a very star-like network structure (Figure 1b) compared to the shape of the network before the pandemic period (Figure 1a). The formation of star-shaped networks is directly related to a higher maximum node degree (De Carvalho & Gupta, 2018). 45 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 For a more global measure of centrality, Onnela et al. (2003) has proposed to calculate mean occupation layer (MOL), which is the average number of links crossed by the centre of the tree (central node) to reach the various other nodes. This is expressed as Equation (7). (7) Where is the MOL for the central node of MST during period and denotes the level of node (other than the central node) in relation to the central node. This level is 1 if is linked to by a direct link, 2 if passes through another node before reaching and so on. The average MOL during the pandemic period dropped significantly to 1.76 compared to a pre-pandemic average of 2.88. Moreover, the average distance of MOL links also decreased by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry became very close to other industries during the pandemic period, both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and confirmed in several studies such as in Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node, the Betweenness centrality is given by Equation (8): (8) Where is the total number of shortest paths from node to node and is the number of shortest paths from node to node through The usefulness of the Betweenness centrality is that some less connected nodes can be very central, i.e.,the fact that they link different parts of the network together. Again, the banking sector was the most central (see Figure 6); it had 36.85 per cent of the shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of the centrality and the systemic risk that may result. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑇𝑇𝑇𝑇 − 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (2) 𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (3) 𝜎𝜎𝜎𝜎𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ �𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑑𝑑𝑑𝑑� 2 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (4) 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 = 1 𝑁𝑁𝑁𝑁−1 × �𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡 ∩ 𝐸𝐸𝐸𝐸(𝑡𝑡𝑡𝑡−1)� (5) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖 = ∑ 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖=1 (6) 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) = 1 𝑁𝑁𝑁𝑁 ∑ ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖=1 (7) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝐵𝐵𝐵𝐵𝐶𝐶𝐶𝐶(𝑖𝑖𝑖𝑖) = ∑ 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗(𝑖𝑖𝑖𝑖) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗 𝑖𝑖𝑖𝑖≠𝑖𝑖𝑖𝑖 (8) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖) 2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑇𝑇𝑇𝑇 − 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (2) 𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (3) 𝜎𝜎𝜎𝜎𝑑𝑑𝑑𝑑 = 1 𝑁𝑁𝑁𝑁−1 ∑ �𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 − 𝑑𝑑𝑑𝑑� 2 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖∈MST (4) 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 = 1 𝑁𝑁𝑁𝑁−1 × �𝐸𝐸𝐸𝐸𝑡𝑡𝑡𝑡 ∩ 𝐸𝐸𝐸𝐸(𝑡𝑡𝑡𝑡−1)� (5) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖 = ∑ 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖=1 (6) 𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) = 1 𝑁𝑁𝑁𝑁 ∑ ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖=1 (7) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑡𝑡𝑡𝑡) ℒ[𝑙𝑙𝑙𝑙𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)] 𝐵𝐵𝐵𝐵𝐶𝐶𝐶𝐶(𝑖𝑖𝑖𝑖) = ∑ 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗(𝑖𝑖𝑖𝑖) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑗𝑗𝑗𝑗 𝑖𝑖𝑖𝑖≠𝑖𝑖𝑖𝑖 (8) 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝜎𝜎𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑖𝑖𝑖𝑖) 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 46 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 Figure 6 Betweenness Centrality of MST Nodes This central weight of the banking industry underscored its importance in the Moroccan economy, and even at the African level where Moroccan banks are among the most solid and most visible. Things may be different in other countries. Yang et al. (2014) found that durable consumer goods were at the heart of the Chinese stock market. Coelho et al. (2007) found that the financial industry was located as a central node in the London Stock Exchange. On the Brazilian stock market, Tabak et al. (2010) showed that telecommunications was positioned at a central location, followed by the materials industry and the finance industry. CONCLUSION This study has provided useful information on how different industry indices have reacted together in light of the pandemic events like that of Covid-19. This reaction was reflected in a sudden rapprochement between industries from the beginning of the Covid-19 pandemic. The construction of the minimum spanning trees (MST) for the pandemic and pre- pandemic periods effectively shows a considerable shrinkage of the tree from the first days of the announcement of pandemic measures. The study of the dynamic evolution of the Moroccan industry indices network shows that the network was relatively stable during the pre- 10 For a more global measure of centrality, Onnela et al. (2003) propose to calculate mean occupation layer (MOL) which is the average number of links crossed by the center of the tree (central node) to reach the various other nodes. 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) = 1 𝑁𝑁 ∑ ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)]𝑁𝑁𝑖𝑖=1 (7) Where 𝑀𝑀𝑀𝑀𝑀𝑀(𝑐𝑐𝑐𝑐𝑡𝑡 ) is the MOL for the central node of MST during period 𝑡𝑡 and ℒ[𝑐𝑐𝑖𝑖 (𝑡𝑡)] denotes the level of node 𝑐𝑐𝑖𝑖 (other than the central node) in relation to the central node. This level is 1 if 𝑐𝑐𝑖𝑖 is linked to 𝑐𝑐𝑐𝑐 by a direct link, 2 if 𝑐𝑐𝑖𝑖 passes through another node before reaching 𝑐𝑐𝑐𝑐 and so on. The average MOL during the pandemic period drops significantly to 1.76 compared to a pre- pandemic average of 2.88. Moreover, the average distance of MOL links also decreases by almost 28 per cent (from 1.23 to 0.89). This shows that the banking industry becomes very close to other industries during the pandemic period both in terms of the decrease in the number of links crossed on average (MOL) and the average distance per link crossed. This double effect explains the topological shrinkage of MST during the pandemic period, initially explained by the MST-Distance indicator and proven by several studies such as Onnela et al. (2003) and Majapa and Gossel (2016). Another indicator given by Barthélemy (2004) to measure the centrality of nodes is the Betweenness centrality which is the fraction of shortest paths passing through a given node. For a node 𝑖𝑖, the Betweenness centrality is given by: 𝐵𝐵𝐵𝐵(𝑖𝑖) = ∑ 𝜎𝜎𝑗𝑗𝑗𝑗(𝑖𝑖)𝜎𝜎𝑗𝑗𝑗𝑗𝑗𝑗≠𝑘𝑘 (8) Where 𝜎𝜎𝑗𝑗𝑘𝑘 is the total number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 and 𝜎𝜎𝑗𝑗𝑘𝑘 (𝑖𝑖) is the number of shortest paths from node 𝑗𝑗 to node 𝑘𝑘 through 𝑖𝑖. The usefulness of Betweenness centrality is that some less connected nodes can be very central by the fact that they link different parts of the network together. Again, the banking sector is the most central (Figure 6); it has 36.85 per cent of shortest paths in the pre-pandemic period and 78.47 per cent in the pandemic period. This shows a particular importance both in terms of centrality and the systemic risk that may result. Figure 6 Betweenness centrality of MST nodes. 47 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 pandemic period, before observing great volatility from the start of the pandemic. This is valid for all the indicators used to study this dynamic. The results show that from one period to another (before pandemic to pandemic), the mean distance dropped by 21.9 per cent, the standard deviation increased by 255 per cent and the mean proximity to the centre of the MST (MOL) decreased to 1.76 links, instead of 2.88 before the pandemic. The other important result is the noted importance of certain industries, and the central role played by the banking industry. In addition to the observed importance of certain industries (“Real estate participation and development”, “Building and construction materials”, “Telecommunication”, “ Food / production”) due to their central weight and their survival in MSTs, the banking industry was positioned as the most central node throughout the period studied. This centrality is perfectly reinforced from the point that it became the only central node during the period of the Covide-19 pandemic. This was also the industry that has survived in all of the MSTs studied. Considering that financial systems in low-income countries tend to be more bank-based than stock market-based, the Moroccan case study is interesting for two reasons. Firstly, for a modest income country like Morocco and with the observed importance of banks as a very central industry in the industry indices network, it can be concluded that it is rather the banking system that is still at the centre of the financial system. Secondly, the importance given by the economic policy in Morocco to the banking industry as a lever for financing and development is compatible with the role that this industry plays in the evolution of the industry indices network. ACKNOWLEDGMENT This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. REFERENCES Ang, A., & Chen, J. (2002). Asymmetric correlations of equity portfolios. Journal of Financial Economics, 63(3), 443–494. https://doi.org/10.1016/S0304-405X(02)00068-5 48 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 Arthur, W. B., Durlauf, S. N., & Lane, D. A. (1997). The economy as an evolving complex system II (1st ed.). Santa Fe Institute Series. Ashraf, B. N. (2020). Stock markets’ reaction to COVID-19: Cases or fatalities? Research in International Business and Finance, 54, 101249. https://doi.org/10.1016/j.ribaf.2020.101249 Aslam, F., Mohmand, Y. T., Ferreira, P., Memon, B. A., Khan, M., & Khan, M. (2020). Networkanalysis of global stock markets at the beginning of the coronavirus disease (Covid-19) outbreak, Borsa Istanbul Review, 20, 49-61. https://doi.org/10.1016/j. bir.2020.09.003 Baker, S. R., Bloom, N., Davis, S. J., Kost, K. J., Sammon, M. C., & Viratyosin, T. (2020). The unprecedented stock market impact of covid- 19, National Bureau of Economic Research, Working Paper Series, number 26945. Barthélemy, M. (2004). Betweenness centrality in large complex networks. Eur. Phys. J. B, 38, 163-168. https://doi.org/10.1140/ epjb/e2004-00111-4 Bonanno, G., Vandewalle, N., & Mantegna, R. N. (2000). Taxonomy of stock market indices. Physical Review E62, 7615-7618. https://doi.org/10.1103/PhysRevE.62.R7615 Bonanno, G., Lillo, F., & Mantegna, R. N. (2001). High-frequency cross-correlation in a set of stocks. Quantitative Finance, 1(1), 96–104. https://doi.org/10.1080/713665554 Coelho, R., Hutzler, S., Repetowicz, P., & Richmond, P. (2007). Sector analysis for a FTSE portfolio of stocks. Physica A. 373, 615-626. https://doi.org/10.1016/j.physa.2006.02.050 De Carvalho, P. J. C., & Gupta, A. (2018). A network approach to unravel asset price co-movement using minimal dependence structure. Journal of Banking and Finance, 91, 119-132. https:// doi.org/10.1016/j.jbankfin.2018.04.012 Drozdz, S., Gruemmer, F., Ruf, F., & Speth, J. (2000). Dynamics of competition between collectively and noise in the stock market. Physica A, 287, 440-449. https://doi.org/10.1016/ S0378- 4371(00)00383-6 Galazka, M. (2011). Characteristics of the polish stock market correlations. International Review of Financial Analysis, 20(1), 1–5. https://doi.org/10.1016/j.irfa.2010.11.002 Gilmore, C. G., Lucey, B. M., & Boscia, M. (2008). An ever-closer union? Examining the evolution of linkages of European equity markets via minimum spanning trees. Physica A, 387. 6319–6329. https://doi.org/10.1016/j.physa.2008.07.012 49 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 Haroon, O., & Rizvi, S. A. R. (2020). Covid-19: Media coverage and financial markets behaviour: A sectoral inquiry. Journal of Behavioral and Experimental Finance, 27, 100343. https://doi. org/10.1016/j.jbef.2020.100343 Khashanah, K., & Miao, L. (2011). Dynamic structure of the US financial systems. Studies in Economics and Finance, 28(4), 321–339. https://doi.org/10.1108/10867371111171564 Liu, H., Manzoor, A., Wang, C., Zhang, L., & Manzoor, Z. (2020). The Covid-19 outbreak and affected countries stock markets response. International Journal of Environmental Research and Public Health, 17(8), 2800. https://doi.org/10.3390/ ijerph17082800 Longin, F., & Solnik, B. (2001). Extreme correlation of international equity markets. The Journal of Finance, 56(2), 649–676. https://doi.org/10.1111/0022-1082 Majapa, M., & Gossel, S. J. (2016).Topology of the South African stock market network across the 2008 financial crisis. Physica A, 445, 35–47. https://doi.org/10.1016/j.physa.2015.10.108 Mantegna, R. N. (1999). Hierarchical structure in financial markets. European Physical Journal B11, 193-197. https://doi. org/10.1007/s100510050929 Musmeci, N., Aste, T., & Di Matteo, T. (2015). Risk diversification: A study of persistence with a filtered correlation-network approach. Journal of Network Theory in Finance, 1(1), 77–98. https://doi.org/10.21314/JNTF.2015.005 Onnela, J. P., Chakraborti, A., Kaski, K., Kertesz, J., & Kanto, A. (2003). Dynamics of market correlations: Taxonomy and portfolio analysis. Physical Review E68, 056110. https://doi. org/10.1103/PhysRevE.68.056110 Sinha, S., & Pan, R. K. (2007). Uncovering the internal structure of the Indian financial market: Cross correlation behaviour in the NSE. Econophysics of Markets and Business Networks. New Economic Windows. Springer, Milano. https://doi. org/10.1007/978-88-470-0665-2_1 Situngkir, H., & Surya, Y. (2005). Indonesian stock market dynamics through ultrametricity of minimum spanning tree. https://ssrn. com/abstract=768204 or http://dx.doi.org/10.2139/ssrn.768204 Tabak, B. M., Serrac, T. R., & Cajueiro, D. O. (2010).Topological properties of stock market networks: The case of Brazil. PhysicaA, 389, 3240–3249. https://doi.org/10.1016 jphysa.2010.04.002 50 The International Journal of Banking and Finance, Vol. 18, Number 1 (January) 2023, pp: 31–50 Tola, V., Lillo, F., Gallegati, M., & Mantegna, R. N. (2008). Cluster analysis for portfolio optimization. Journal of Economic Dynamics and Control, 32, 235-258. https://doi.org/10.1016/j. jedc.2007.01.034 Tumminello, M., Lillo, F., & Mantegna, R. N. (2010). Correlation, hierarchies, and networks in financial markets. Journal of Economic Behavior and Organization, 75, 40–58. https://doi. org/10.48550/arXiv.0809.4615 Yang, R., Lia, X., & Zhang, T. (2014). Analysis of linkage effects among industry sectors in China’s stock market before and after the financial crisis. Physica A, 411, 12–20. https://doi. org/10.1016/j.physa.2014.05.072 Zhang, D., Hu, M., & Ji, Q. (2020). Financial markets under the global pandemic of Covid-19, Finance Research Letters, 36,101528. https://doi.org/10.1016/j.frl.2020.101528