Investigating the Relation Between Companies with Topological Analysis of a Network of Stock Exchange in Brazil

Abstract

B3 (Brasil, Bolsa, Balcão) is the official stock exchange in Brazil and plays a key role in the world financial market. Stock exchange allows people and companies to relate through the shareholding and the purchase and sale of shares. The study of the relationship between people and companies can reveal valuable information about the operation of the stock exchange and, consequently, the financial market as a whole. In this work, the relations in B3 are modeled as a network, in which the vertices represent companies and people and the edges represent shareholdings. From the built network, several analyzes are performed with the objective of understanding and characterizing the patterns found in relationships. Investigation on the topology of the network is performed under different perspectives, such as the centrality of the vertices, organization of vertices in communities, the robustness and the diffusion of influence. The results show a strong community structure in the B3 network and, even though the network is fragile for the removal of vetices, the definition of the criterion of vertices to be chosen as a target can be determinant in the characterization of the robustness.