Percolation on bipartite scale-free networks

H. Hooyberghs, B. Van Schaeybroeck and J.O. Indekeu

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 15, 2920-2929

Abstract: Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual-contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with a probability proportional to (kq)−α, where α is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin–Kasteleyn construction which provides a link between our model and a limit of the Potts model.

Keywords: Scale-free networks; Percolation; Bipartite networks; Sexual-contact network (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:15:p:2920-2929

DOI: 10.1016/j.physa.2009.12.068

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