Observation of Frustrated Correlation Structure in a Well-Developed Financial Market

We approach the correlation structure in the Tokyo Stock Exchange (TSE) market through a concept of community of network. To construct a network, the correlation matrix of stock price changes, purified by random matrix theory, is regarded as an adjacency matrix. The stock correlation network thus constructed has negatively weighted links as well as positively weighted links. By extracting groups in which stocks are mainly interconnected by positive links, we find that the stocks decomposed into four comoving groups forming communities, three of which are strongly anticorrelated to each other, and the remainder is comparatively neutral to the rest of the communities. The conflicting triangle relationship between communities may cause complicated behavior in a well-development market such as TSE. Additionally, it is observed that some industrial sectors form distinctive coherent groups and others are separated to competing communities.