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

Maksim Kitsak, Shlomo Havlin, Gerald Paul, Massimo Riccaboni (massimo.riccaboni@imtlucca.it), Fabio Pammolli (fabio.pammolli@polimi.it) 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: E17 L00 L25 L60 L63 L65 O30 (search for similar items in EconPapers)
Date: 2007-05-31
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published in Physical Review E 5.75(2007): pp. 056115

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