Establishment of a Non-Linear Financial Network Based on its Typological Characteristics Based on Graph Theory (A Study in Tehran Stock Exchange)

The purpose of this study is to introduce a financial network based on non-linear relationships between stocks to optimize the portfolio of investors,identify the leaders of the Iranian stock market using centrality criteria and finally clustering non-linear financial network.In this study,the top 100 companies listed on the stock exchange with the highest capital registered in the 11-year period (December 2009 to January 2020) were selected.The results show that according to the degree centrality, the stocks of Sepahan Cement,Omid Capital Financing,and Omid Investment,according to the criterion of closeness centrality,Ghadir investment stocks, investment of National Development and Khuzestan Steel, According to the closeness centrality,Ghadir investment stocks,National Development and Khuzestan Steel Investment Group, according to the betweenness centrality,Ghadir Investment stocks, Sepahan Cement and National Development Investment and according to the bottleneck centrality, the stocks of Khuzestan Steel,Sepahan Cement and International Building Development have the most impact on the stock market and were identified as market leaders. To categorize the top stocks, the fast greedy algorithm was used, in which the network was divided into 11 clusters, and each of these clusters represents the largest relationship between the shares of companies in the financial network.