Universal Journal of Accounting and Finance 7(4): 106-121, 2019 DOI: 10.13189/ujaf.2019.070403 http://www.hrpub.org Topological Structure of Stock Market Networks during Financial Turbulence: Non-Linear Approach Arash Sioofy Khoojine * , Han Dong School of mathematics and statistics, Shanghai Jiao Tong University, China Received November 01, 2019; Revised December 09, 2019; Accepted December 17, 2019 Copyright c 2019 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract In this paper, researchers utilize mutual infor- mation and distance covariance to establish the minimum spanning tree of the financial network of log-returns and trading volumes of the top 96 companies of the United States stock market listed on S&P 100 index. Researchers analyze the United States stock market’s turbulence during 2015 -2016, employing the data from January 2012 to July 2018. For investigating the turbulence, researchers construct three minimum spanning trees of the pre-turbulence, turbulence and post-turbulence. The findings represent that the degree distribution follows the power law and the minimum spanning tree of pre-turbulence contains a notable difference in topo- logical characteristics and network’s measures such degree ratio, betweenness, closeness, eigenvector centrality, node eccentricity, node strength, node domination compared with turbulence and post-turbulence minimum spanning trees. Moreover, the minimum spanning trees constructed by two methods of mutual information and distance covariance are different in topological characteristics and the network’s behavior. Besides, the pre-turbulence and post-turbulence networks are robust against nodes attack, and turbulence network is tenuous against it. Keywords Statistical Network Analysis, Mutual Informa- tion, Distance Covariance, Symbolic Time Series, Financial Turbulence 1 Introduction 1.1 Brief Literature Review In the real world, most of the complex systems have been represented by complex networks [19]. Intrinsically, the stock market has been explained as a complex system. There exist an intricate relationship between stocks, which causes price os- cillation. During the last two decades, researchers have scruti- nized stock markets by forming the stock correlation networks, of which the nodes represent stocks and edges between nodes are price oscillation relationships of stocks [18]. Scrutinizing financial systems, particularly stock price mar- kets, using the complex networks perspective has become one of the most widespread fields within econophysics. Addition- ally, a similar tendency is nowadays coming into sight within the econometrics and finance community researchers. Classifying methodologically, various methods have been implemented to numerous stock markets, Heimo et al., and Gan et al. use Pearson’s correlation coefficient to analyze the New York stock exchange [12, 10], Huang et al. use a thresh- old method to construct China’s stock correlation network and analyze the network’s structural properties and topological sta- bilities [15]. Tabak et al. investigate the topological properties of the Brazilian stock market networks by building the mini- mum spanning tree. Their results suggest stocks tend to clus- ter by sector [23]. Galazka studies network structure of the Polish Stock Market using Minimum Spanning Tree (MST) and Weighted Random Graph (WRG) and compares them [9]. Coronnello et al. apply random matrix theory and hierarchi- cal clustering techniques to a portfolio of stocks at the London Stock Exchange. Results have shown that the application of just a distinct method is not enough to extract all the economic information in the correlation coefficient matrix of a stock port- folio [3]. Zhuang et al. build a minimum spanning tree of CSI 300 index of the Shanghai and Shenzhen Stock markets and analyze its structure [25]. A few articles have been published about the behavior of networks during financial crises. Majapa and Gossel, look over the topological characteristics of financial networks before and after the 2008 financial crisis of South African stock market. They use correlations networks of the daily closing prices of the South African Top 100 companies from June 2003 to June 2013 to create a minimum spanning tree of before, during and after the financial crisis. The findings reveal that the network shrinks during the crisis period and expands afterwards [17]. Nobi et al., analyze the effects of the 2008 global financial cri- sis on financial networks of the Korean financial market around the crisis period. They contemplate the prices of stocks belong- ing to KOSPI 200 (Korea Composite Stock Price Index 200) for three periods, before, during and after the crisis. Threshold CITE THIS PAPER [1] Arash Sioofy Khoojine , Han Dong , "Topological Structure of Stock Market Networks during Financial Turbulence: Non-Linear Approach," Universal Journal of Accounting and Finance, Vol. 7, No. 4, pp. 106 - 121, 2019. DOI: 10.13189/ujaf.2019.070403.