Mathematical Analysis of Economic Networks
*1The Canon Institute for Global Studies, 11th Floor, Shin-Marunouchi Building, 1-5-1 Marunouchi, Chiyoda-ku, Tokyo
*2The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo
Firms build business relationships through economic activities. PageRank algorithm and motif analysis are applied to Japanese inter-firm network which consists of about one million firms and four million directed links. We show scale-free degree distribution and similarities between degree and PageRank. By comparing with randomized networks, we find that PageRank correlates significantly with the growth rate which is hardly observed with other quantities. We also find that Vshaped triads are network motifs, while feedforward and feedback loop are anti-motifs. By defining roles in the subgraph according to structural equivalence, we detect the significance profile of roles characterizing the industry sector. The taxonomy of industries obtained from the profiles is economically meaningful. These empirical findings may serve to provide an easily interpretable view of the entire inter-firm network and to improve the efficiency and safety of economic systems.