Two complementary representations of a scale-free network

2004/02/29 by J. C. Nacher, T. Yamada, S. Goto +2
Physics and Astronomy · #physics.bio-ph #cond-mat.dis-nn #cond-mat.stat-mech #physics.data-an

paper · pdf · doi:10.1016/j.physa.2004.09.013

published as Physica A 349 (2005) 349-363 · 18 pages, 8 figures. Minor changes. One figure added

arxiv created 2005/04/13 · arxiv updated 2009/12/01

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 to 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 to real networks as metabolic networks, protein-protein interaction network and World Wide Web.

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