# Characterization of the community structure in a large-scale production network in Japan

## TL;DR

This paper analyzes a large-scale Japanese production network, revealing its community structure, local interactions, and heterogeneity in inter-community relationships, providing insights into economic organization.

## Contribution

It offers a detailed characterization of community structures in a large production network, highlighting local interactions and sectoral and regional over-expressions.

## Key findings

- Community structure exhibits tree-like topology in small communities
- Approximately 40% of small firms interact mainly within their communities
- Inter-community link weights are highly heterogeneous

## Abstract

Inter-firm organizations, which play a driving role in the economy of a country, can be represented in the form of a customer-supplier network. Such a network exhibits a heavy-tailed degree distribution, disassortative mixing and a prominent community structure. We analyze a large-scale data set of customer-supplier relationships containing data from one million Japanese firms. Using a directed network framework, we show that the production network exhibits the characteristics listed above. We conduct detailed investigations to characterize the communities in the network. The topology within smaller communities is found to be very close to a tree-like structure but becomes denser as the community size increases. A large fraction (~40%) of firms with relatively small in- or out-degrees have customers or suppliers solely from within their own communities, indicating interactions of a highly local nature. The interaction strengths between communities as measured by the inter-community link weights follow a highly heterogeneous distribution. We further present the statistically significant over-expressions of different prefectures and sectors within different communities.