Community Detection of Dynamic Complex Networks in Stock Markets Using Hybrid Methods (RMT‐CN‐LPAm+ and RMT‐BDM‐SA)

Abstract

A stock market represents a large number of interacting elements, leading to complex hidden interactions. It is very challenging to find a useful method to detect the detailed dynamical complex networks involved in the interactions. For this reason, we propose two hybrid methods called RMT-CN-LPAm+ and RMT-BDM-SA (RMT, random matrix theory; CN, complex network; LPAm+, advanced label propagation algorithm; BDM, block diagonal matrix; SA, simulated annealing). In this study, we investigated group mapping in the S&P 500 stock market using these two hybrid methods. Our results showed the good performance of the proposed methods, with both the methods demonstrating their own benefits and strong points. For example, RMT-CN-LPAm+ successfully identified six groups comprising 485 involved nodes and 17 isolated nodes, with a maximum modularity of 0.62 (identified more groups and displayed more maximum modularity). Meanwhile, RMT-BDM-SA provided useful detailed information through the decomposition of matrix C into Cm (market-wide), Cg (group), and Cr (noise). Both hybrid methods successfully performed very detailed community detection of dynamic complex networks in the stock market.