How clustering affects the bond percolation threshold in complex networks

TL;DR

This paper analytically investigates how clustering in networks, characterized by triangles, influences the bond percolation threshold, revealing that increased clustering raises the threshold and reduces network resilience.

Contribution

It provides an analytical study showing that clustering increases the bond percolation threshold in complex networks, extending understanding of network robustness.

Findings

Clustering raises the bond percolation threshold.

Triangles decrease network resilience to random edge removal.

Analytical models quantify the impact of clustering.

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).