Network motifs in an inter-firm network

Firms build business relationships during economic activities. The goal of this paper is to clarify production mechanisms and economic functions by identifying characteristic patterns of inter-firm interactions. In this paper, we empirically analyze an inter-firm network consisting of about one million firms and four million directed links, in order to specify network motifs, which are small subgraphs that occur more frequently than expected in a randomly generated network. We found that V-shaped triads are network motifs, while feedforward and feedback loop are anti-motifs. By defining roles in the subgraph according to structural equivalence, we also detected 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.