We present a new approach to understanding credit relationships between
commercial banks and quoted firms, and with this approach, examine the temporal
change in the structure of the Japanese credit network from 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 a set of scores of banks and
firms, which can be calculated by solving an eigenvalue problem determined by
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