Abstract
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.
