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.
scale-free networks, hierarchical organization, clustering
Hierarchies, Scaling laws (Statistical physics), Topology
The American Physical Society
©2003 The American Physical Society
Ravasz, Erzsébet and Barabási, Albert-László, "Hierarchical organization in complex networks" (2003). Physics Faculty Publications. Paper 113. http://hdl.handle.net/2047/d20000686
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