Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks

Maksim Kitsak, Shlomo Havlin, Gerald Paul, Massimo Riccaboni (), Fabio Pammolli () and H. Eugene Stanley

MPRA Paper from University Library of Munich, Germany

Abstract: We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution P(C) ~ C^δ. We find that for non-fractal scale-free networks δ = -2, and for fractal scale-free networks δ = -2 + 1/dB, where dB is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N = 6776), yeast (N = 1458), WWW (N = 2526), and a sample of Internet network at AS level (N = 20566), where N is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length ℓ*, separating fractal and non-fractal regimes, scales with dimension dB of the network as p−1/dB, where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p.

Keywords: Interfirm networks; R&D collaborations; Pharmaceutical industry; ICT. (search for similar items in EconPapers)
JEL-codes: L65 L25 O30 E17 L60 L00 L63 (search for similar items in EconPapers)
Date: Written
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Published in Physical Review E 5.75(2007): pp. 056115

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