Heterogeneous Economic Networks

Abstract

Summary. The Japanese shareholding network at the end of March 2002 is studied. To understand the characteristics of this network intuitively, we visualize it as a directed graph and an adjacency matrix. Especially detailed features of networks concerned with the automobile industry sector are discussed by using the visualized networks. The shareholding network is also considered as an undirected graph, because many quantities characterizing networks are defined for undirected cases. For this undirected shareholding network, we show that a degree distribution is well fitted by a power law function with an exponential tail. The exponent in the power law range is γ = 1.8. We also show that the spectrum of this network follows asymptotically the power law distribution with the exponent δ = 2.6. By comparison with γ and δ, we find a scaling relation δ = 2γ − 1. The reason why this relation holds is attributed to the local tree-like structure of networks. To clarify this structure, the correlation between degrees and clustering coefficients is considered. We show that this correlation is negative and fitted by the power law function with the exponent α = 1.1. This guarantees the local tree-like structure of the network and suggests the existence of a hierarchical structure. We also show that the degree correlation is negative and follows the power law function with the exponent ν = 0.8. This indicates a degree-nonassortative network, in which hubs are not directly connected with each other. To understand these features of the network from the viewpoint of a company's growth, we consider the correlation between the degree and the company's total assets and age. It is clarified that the degree and the company's total assets correlate strongly, but the degree and the company's age have no correlation.

Detecting overlapping community structure: Estonian network of payments

“…Networks play an important role in a wide range of economic and social phenomena and the use of techniques and methods from graph theory has permitted economic network theory to expand the knowledge and understanding of economic phenomena in which the embeddedness of individuals or agents in their social or economic interrelations cannot be ignored [4]. For example, Souma et al [5] studied a shareholder network of Japanese companies where the authors analyzed the companies' growth through economic networks dynamics. Other examples of interesting applications of complex networks in economics are provided by the regional investment or ownership networks where European company-tocompany investment stocks show power-law distributions that allow predicting the investments that will be received or made in specific regions, based on the connectivity and transactional activity of the companies [6][7].…”

Shareholding Networks in Japan

“…This was calculated by Ref. [5] for the Japanese shareholding networks at the end of March 2002, in which k nn (k) ∝ k −ν was obtained with the exponent ν = 0.8. This means that hubs are not directly connected to each other in this network, i.e., it's a degree non-assortative network.…”

“…The clustering coefficient of node i, C i , is the fraction of these allowable edges that actually exist for e i , i.e., C i = 2e i /k i (k i − 1). This has been calculated for an undirected shareholding network by using the same data used in this article [5], and it has been shown that the clustering coefficient follows the power law distribution, C(k) ∝ k −α , with the exponent α = 1.1. Such a scaling property of the distribution of clustering coefficients has also been observed in biological networks, and this has motivated the concept of hierarchical networks [10] [11].…”

“…Recently, the study of complex networks has revealed the true structure of real-world networks [1] [2]. Gross networks such as interindustry relations have been considered in the macro economy, but the detailed structures of networks constructed from entities in the micro economy have not been clearly elucidated [3][4] [5] [6].…”

Change of ownership networks in Japan

“…This development also holds true in the field of econophysics. Such studies have investigated business networks [9], shareholding networks [10,11,12,5], world trade networks [6,7], and corporate board networks [2,4].…”