dorsal/arxiv
View SchemaHeterogeneous Economic Networks
| Authors | Wataru Souma, Yoshi Fujiwara, Hideaki Aoyama |
|---|---|
| Categories | |
| ArXiv ID | physics/0502005 |
| URL | https://arxiv.org/abs/physics/0502005 |
Abstract
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 gamma=1.8. We also show that the spectrum of this network follows asymptotically the power law distribution with the exponent delta=2.6. By comparison with gamma and delta, we find a scaling relation delta=2gamma-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 alpha=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 nu=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.
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"abstract": "The Japanese shareholding network at the end of March 2002 is studied. To\nunderstand the characteristics of this network intuitively, we visualize it as\na directed graph and an adjacency matrix. Especially detailed features of\nnetworks concerned with the automobile industry sector are discussed by using\nthe visualized networks. The shareholding network is also considered as an\nundirected graph, because many quantities characterizing networks are defined\nfor undirected cases. For this undirected shareholding network, we show that a\ndegree distribution is well fitted by a power law function with an exponential\ntail. The exponent in the power law range is gamma=1.8. We also show that the\nspectrum of this network follows asymptotically the power law distribution with\nthe exponent delta=2.6. By comparison with gamma and delta, we find a scaling\nrelation delta=2gamma-1. The reason why this relation holds is attributed to\nthe local tree-like structure of networks. To clarify this structure, the\ncorrelation between degrees and clustering coefficients is considered. We show\nthat this correlation is negative and fitted by the power law function with the\nexponent alpha=1.1. This guarantees the local tree-like structure of the\nnetwork and suggests the existence of a hierarchical structure. We also show\nthat the degree correlation is negative and follows the power law function with\nthe exponent nu=0.8. This indicates a degree-nonassortative network, in which\nhubs are not directly connected with each other. To understand these features\nof the network from the viewpoint of a company\u0027s growth, we consider the\ncorrelation between the degree and the company\u0027s total assets and age. It is\nclarified that the degree and the company\u0027s total assets correlate strongly,\nbut the degree and the company\u0027s age have no correlation.",
"arxiv_id": "physics/0502005",
"authors": [
"Wataru Souma",
"Yoshi Fujiwara",
"Hideaki Aoyama"
],
"categories": [
"physics.soc-ph"
],
"title": "Heterogeneous Economic Networks",
"url": "https://arxiv.org/abs/physics/0502005"
},
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