Abstract

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale-free topology. In hierarchical networks, the degree of clustering characterizing the different groups follows a strict scaling law, which can be used to identify the presence of a hierarchical organization in real networks. We find that several real networks, such as the Worldwideweb, actor network, the Internet at the domain level, and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems.

Notes

Originally published in Physical Review E 67(2), 2003. doi:10.1103/PhysRevE.67.026112

Keywords

scale-free networks, hierarchical organization, clustering

Subject Categories

Hierarchies, Scaling laws (Statistical physics), Topology

Disciplines

Physics

Publisher

The American Physical Society

Publication Date

2-2003

Rights Holder

©2003 The American Physical Society

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