Community Structure of a Large-Scale Production Network in Japan

This chapter analyzes nationwide supplier–buyer relationship data for nearly a million firms and 4 million transactions in Japan. The production network constructed by firms through their transaction relations reflects the characteristics of economic activities in Japan. For an intuitive understanding of the network structure, we first visualize the network in three-dimensional space using a spring–electrostatic model. In this model, we replace nodes (firms) and links (transaction relations) by particles with identical charges and springs. This visualization shows that the network is highly heterogeneous, with some firms being tightly connected and forming groups, between which there are much looser connections. Such industrial communities are identified here using algorithms that maximize modularity, which measures the share of links encircled by a given partition of nodes, with reference to the expected share of intra-links for corresponding random networks with the same node partitions. Since major communities thereby detected are still very heterogeneous, the detection of communities is repeated within them. The 10 largest communities and their principal sub-communities are then characterized by areal and industry sectoral attributes of firms. In addition, how closely the sub-communities are related to each other is quantified by introducing a metric of “distance” between them. Finally, the hierarchical relationship between the communities is clarified by considering directional features of the transactions.

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