Structure and Temporal Change of Credit Network between Banks and Large Firms in Japan

Credit relationships between commercial banks and quoted firms are studied for the structure and its temporal change from the year 1980 to 2005. At each year, the credit network is regarded as a weighted bipartite graph where edges correspond to the relationships and weights refer to the amounts of loans. Reduction in the supply of credit affects firms as debtor, and failure of a firm influences banks as creditor. To quantify the dependency and influence between banks and firms, we propose to define a set of scores of banks and firms, which can be calculated by solving an eigenvalue problem determined the weight of the credit network. We found that a few largest eigenvalues and corresponding eigenvectors are significant by using a null hypothesis of random bipartite graphs, and that the scores can quantitatively describe the stability or fragility of the credit network during the 25 years