Analytical results for bond percolation and k-core sizes on clustered networks

James P. Gleeson and Sergey Melnik
Phys. Rev. E 80, 046121 – Published 26 October 2009

Abstract

An analytical approach to calculating bond percolation thresholds, sizes of k-cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated using a generalization of Trapman’s [P. Trapman, Theor. Popul. Biol. 71, 160 (2007)] model of cliques embedded in treelike random graphs. The resulting networks have arbitrary degree distributions and tunable degree-dependent clustering. The effect of clustering on the bond percolation thresholds for networks of this type is examined and contrasted with some recent results in the literature. For very high levels of clustering the percolation threshold in these generalized Trapman networks is increased above the value it takes in a randomly wired (unclustered) network of the same degree distribution. In assortative scale-free networks, where the variance of the degree distribution is infinite, this clustering effect can lead to a nonzero percolation (epidemic) threshold.

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  • Received 4 December 2008

DOI:https://doi.org/10.1103/PhysRevE.80.046121

©2009 American Physical Society

Authors & Affiliations

James P. Gleeson and Sergey Melnik

  • Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

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Issue

Vol. 80, Iss. 4 — October 2009

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