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Two complementary representations of a scale-free network

Author

Listed:
  • Nacher, J.C.
  • Yamada, T.
  • Goto, S.
  • Kanehisa, M.
  • Akutsu, T.

Abstract

Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like P(k)≈k-γ, where P(k) denotes the frequency of the nodes that are connected to k other nodes. Here we have carried out a study on scale-free networks, where a line graph transformation (i.e., edges in an initial network are transformed into nodes) is applied on a power-law distribution. Our results indicate that a power-law distribution as P(k)≈k-γ+1 is found for the transformed network together with a peak for low-degree nodes. In the present work, we show a parametrization of this behaviour and discuss its application on real networks as metabolic networks, protein–protein interaction network and World Wide Web.

Suggested Citation

  • Nacher, J.C. & Yamada, T. & Goto, S. & Kanehisa, M. & Akutsu, T., 2005. "Two complementary representations of a scale-free network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 349-363.
    • Handle: RePEc:eee:phsmap:v:349:y:2005:i:1:p:349-363
    DOI: 10.1016/j.physa.2004.09.013
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    Cited by:

    1. Krawczyk, M.J. & Muchnik, L. & Mańka-Krasoń, A. & Kułakowski, K., 2011. "Line graphs as social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2611-2618.

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