The objective of this study is to shed new light on the industrial flow structure embedded in microscopic supplier-buyer relations. We first construct directed networks from actual data from interfirm transaction relations in Japan; as one example, the dataset compiled by the Tokyo Shoko Research, Ltd. in 2016 contains five million links between one million firms. Then, we analyze the industrial flow structure of such a large-scale network with a special emphasis on its hierarchy and circularity. The Helmholtz-Hodge decomposition enables us to break down the flow on a directed network into two flow components: gradient flow and circular flow. The gradient flow between a pair of nodes is given by the difference of their potentials obtained by the Helmholtz-Hodge decomposition. The gradient flow runs from a node with higher potential to a node with lower potential; hence, the potential of a node shows its hierarchical position in a network. On the other hand, the circular flow component illuminates feedback loops built in a network. The potential values averaged over firms classified by the major industrial category describe hierarchical characteristics of sectors. The ordering of sectors according to the potential agrees well with the general idea of the supply chain. We also identify industrially integrated clusters of firms by applying a flow-based community detection method to the extracted circular flow network. We then find that each of the major communities is characterized by its main industry, forming a hierarchical supply chain with feedback loops by complementary industries such as transport and services.

This paper studies the structure of the Japanese production network, which includes one million firms and five million supplier-customer links. This study finds that this network forms a tightly-knit structure with a core giant strongly connected component (GSCC) surrounded by IN and OUT components constituting two half-shells of the GSCC, which we call awalnut structure because of its shape. The hierarchical structure of the communities is studied by the Infomap method, and most of the irreducible communities are found to be at the second level. The composition of some of the major communities, including overexpressions regarding their industrial or regional nature, and the connections that exist between the communities are studied in detail. The findings obtained here cause us to question the validity and accuracy of using the conventional input-output analysis, which is expected to be useful when firms in the same sectors are highly connected to each other.

This paper studies the structure of the Japanese production network, which includes one million firms and five million supplier-customer links. This study finds that this network forms a tightly-knit structure with a core giant strongly connected component (GSCC) surrounded by IN and OUT components constituting two half-shells of the GSCC, which we call awalnut structure because of its shape. The hierarchical structure of the communities is studied by the Infomap method, and most of the irreducible communities are found to be at the second level. The composition of some of the major communities, including overexpressions regarding their industrial or regional nature, and the connections that exist between the communities are studied in detail. The findings obtained here cause us to question the validity and accuracy of using the conventional input-output analysis, which is expected to be useful when firms in the same sectors are highly connected to each other.

This study examines how research collaboration of firms affects the quality of their innovation outcomes using comprehensive patent data for firms in the world from 1991 to 2010. Identifying research collaboration by co-patenting relationships, we find that research collaboration with other firms, particularly with foreign firms, leads to substantial improvement in innovation quality. We also observe a positive effect of the brokerage in the global network, especially for firms with international collaboration links. These results are applicable to the effect on the quality of innovation achieved individually without any collaboration. Therefore, our findings emphasize the importance of links with a variety of partners, particularly with foreign partners to improve innovation performance. Finally, we find that the collaboration effect is larger in the 2000s than in the 1990s and varies depending on firm size and across countries.

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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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