Hierarchical Communities in the Walnut Structure of the Japanese Production Network

The structure of Japanese production network with one million firms and five million supplier-customer links is studied. It is found that they form a tightly-knit structure with a core giant strongly connected component (GSCC) surrounded by IN and OUT components constituting two half-shells after the GSCC, which we name 'Walnut structure' after its shape. The hierarchical structure of communities is studied by Infomap method and most of the irreducible communities are found to be on the second level. Composition of some of the major communities, including overexpressions of industrial and regional nature, as well as connections between the communities, is studied in detail. The findings obtained here cast doubt on the validity and accuracy of the conventional input-output analysis, which is expected to be useful if firms in the same sectors would be well connected with each other