Centrality measure of complex networks using biased random walks
Department of Physics and Research Institute for Basic
Sciences, Kyung Hee University, Seoul, 130-701, Korea
Revised: 23 January 2009
Published online: 14 March 2009
We propose a novel centrality measure based on the dynamical properties of a biased random walk to provide a general framework for the centrality of vertex and edge in scale-free networks (SFNs). The suggested centrality unifies various centralities such as betweenness centrality (BC), load centrality (LC) and random walk centrality (RWC) when the degree, k, is relatively large. The relation between our centrality and other centralities in SFNs is clearly shown by both analytic and numerical methods. Regarding to the edge centrality, there have been few established studies in complex networks. Thus, we also provide a systematic analysis for the edge BC (LC) in SFNs and show that the distribution of edge BC satisfies a power-law. Furthermore we also show that the suggested centrality measures on real networks work very well as on the SFNs.
PACS: 89.75.Hc – Networks and genealogical trees / 05.40.Fb – Random walks and Levy flights / 89.20.-a – Interdisciplinary applications of physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009