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Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks

Kitsak, Maksim and Havlin, Shlomo and Paul, Gerald and Riccaboni, Massimo and Pammolli, Fabio and Stanley, H. Eugene Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks. Physical Review E, 75 (5). 056115. ISSN 1539-3755 (2007)

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Abstract

We study the betweenness centrality of fractal and nonfractal 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 nonfractal models. We also show that nodes of both fractal and nonfractal scale-free networks have power-law betweenness centrality distribution P(C)∼C−δ. We find that for nonfractal 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 the autonomous system 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 nonfractal networks upon adding random edges to a fractal network. We show that the crossover length ℓ*, separating fractal and nonfractal 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.

Item Type: Article
Identification Number: 10.1103/PhysRevE.75.056115
Additional Information: © 2007 The American Physical Society
Uncontrolled Keywords: PACS: 89.75.Hc
Subjects: Q Science > QC Physics
Research Area: Economics and Institutional Change
Depositing User: Users 2 not found.
Date Deposited: 30 Jun 2011 14:26
Last Modified: 18 Dec 2014 15:44
URI: http://eprints.imtlucca.it/id/eprint/643

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