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

Listed author(s):
  • Kitsak, Maksim
  • Havlin, Shlomo
  • Paul, Gerald
  • Riccaboni, Massimo
  • Pammolli, Fabio
  • Stanley, H. Eugene

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15907.

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Date of creation: 31 May 2007
Publication status: Published in Physical Review E 5.75(2007): pp. 056115
Handle: RePEc:pra:mprapa:15907
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  1. Orsenigo, L. & Pammolli, F. & Riccaboni, Massimo, 2001. "Technological change and network dynamics: Lessons from the pharmaceutical industry," Research Policy, Elsevier, vol. 30(3), pages 485-508, March.
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