Percolation on bipartite scale-free networks

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 netw...

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Bibliographic Details
Published in:Physica A 2010-08, Vol.389 (15), p.2920-2929
Main Authors: Hooyberghs, H., Van Schaeybroeck, B., Indekeu, J.O.
Format: Article
Language:English
Subjects:
Bipartite networks
Failure
Links
Mathematical analysis
Mathematical models
Networks
Percolation
Running
Scale-free networks
Sexual-contact network
Statistical mechanics
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Summary: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 ( k q ) − 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.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2009.12.068