Abstract
We study group correlation structures of financial markets in Japan and U.S. from a
network-theoretic point of view. The correlationmatrix of stock price changes, purified by the random
matrix theory, is regarded as an adjacency matrix for a network. The weighted links in the networks
thus constructed can have negative sign corresponding to anticorrelation between stocks. To identify
groups in such a network, we search for the optimum decomposition of nodes which maximizes the
total sum of weights of links inside groups. We then find that the network of Tokyo Stock Exchange is
decomposed into four groups. The stock prices comove almost perfectly inside the groups and move
oppositely across the groups. Also we apply the same analysis to the S&P 500 stocks. The U.S. stock
market shows frustrated behavior similar to that embedded in the Japanese market.
