Hierarchical and Circular Flow Structure of Interfirm Transaction Networks in Japan

Abstract

The objective of this study is to shed new light on industrial flow structure embedded in microscopic supplier-buyer relations. We first construct directed networks from actual data of interfirm transaction relations in Japan containing five million links between one million firms. And then we analyze the industrial flow structure of such large-scale networks with a special emphasis on its hierarchy and circularity. The Helmholtz-Hodge decomposition enables us to break down flow on a directed network into two flow components: potential flow and circular flow. The potential flow between a pair of nodes is given by difference of their potentials, and hence, the potential of a node quantifies its hierarchical position in a network. On the other hand, the circular flow component illuminates feedback loops built in a network; it can be an engine of economic growth in the industrial system. The potential values averaged over firms classified by the major category of industry describe hierarchical characteristics of the sectors. Their ordering from upstream to downstream agrees well with the general idea on the supply chain. We also identify dominant clusters of firms forming feedback loops by applying a flow-based community detection method to the extracted circular flow network.