How clustering affects the bond percolation threshold in complex networks

Abstract

The question of how clustering (non-zero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modelling highly-clustered networks are employed here to analytically study the bond percolation threshold. In comparison to the threshold in an unclustered network with the same degree distribution and correlation structure, the presence of triangles in these model networks is shown to lead to a larger bond percolation threshold (i.e. clustering \emph{increases} the epidemic threshold or \emph{decreases} resilience of the network to random edge deletion).

10 pages, 4 figures. Added new Appendix D, updated figures.

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