Multiscale Community Analysis of a Production Network of Firms in Japan

Abstract

We investigate a production network constructed by about 800 thousand firms in Japan through four million transaction relations with focus on its community structure. Communities detected by maximizing modularity often contain nodes with common properties such as characterized by regions or industry sectors. However, the modularity optimization approach suffers from the resolution limit problem; small but important communities tend to be combined into a single large group. To unfold such hidden structure, the community detection was reiterated within each of major communities. Then it was found that the communities were composed of well-defined subcommunities, some of which were separated into smaller groups with more specified regions or industry sectors. Furthermore, a new tool is proposed for measuring the strength of relations between those subcommunities. It is shown to be useful to elucidate the multiscale structure of the network.