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.

Social networks often has the graph structure of giant strongly connected component (GSCC) and its upstream and downstream portions (IN and OUT), known as a bow-tie structure since a pioneering study on the World Wide Web (WWW). GSCC, on the other hand, has community structure, namely tightly knitted clusters, reflecting how the networks developed in time. By using our visualization of enhanced multidimensional scaling (MDS) and force-directed graph drawing for large and directed graphs, we discovered that a bow-tie in the WWW usually has clusters, which are locally-located mini bow-ties that are loosely connected to each other, resulting in a formation of GSCC as a whole. To quantify the mutual connectivity among such local bow-tie, we define a quantity to measure how a local bow-tie connects to others in comparison with random graphs. We found that there are striking difference between the WWW and other social and artificial networks including a million firms' nationwide supply chain network in Japan and thousands of symbols' dependency in the programming language of Emacs LISP, in which a global bow-tie exits. Presumably the difference comes from a self-similar structure and development of the WWW speculated by others.

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The interactions among macroprices with leads and lags play a significant role in explaining the behavior of an aggregate price index. Thus, to understand inflation and deflation, it is essential to explore the mechanism according to which these macroprices interact with each other. On the basis of a new method, we show that, irrespective of the sources of shocks, a robust flow of changes occurs in domestic prices from upstream to downstream. Moreover, we demonstrate that macroprices change in clusters, and we identify these clusters. Firms are not symmetric. Overall, our analysis suggests that the inertia arising from input/output linkages in production explains the behavior of aggregate prices.

The interactions among macroprices with leads and lags play a significant role in explaining the behavior of an aggregate price index. Thus, to understand inflation and deflation, it is essential to explore the mechanism according to which these macroprices interact with each other. On the basis of a new method, we show that, irrespective of the sources of shocks, a robust flow of changes occurs in domestic prices from upstream to downstream. Moreover, we demonstrate that macroprices change in clusters, and we identify these clusters. Firms are not symmetric. Overall, our analysis suggests that the inertia arising from input/output linkages in production explains the behavior of aggregate prices.

No abstract