Classification of scale-free networks

Details Classification of scale-free networks Classification of scale-free networks

2002-05-11

arxiv.org/abs/cond-mat/0205232v2

Proc. Natl. Acad. Sci. USA 99, 12583 (2002)

Physics

Condensed Matter

Statistical Mechanics

6 Pages, 6 Figures, 1 table

Scientific paper

10.1073/pnas.202301299

While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is robust and use it to classify the scale-free networks. We have observed two universality classes with \eta \approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.

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