Clustering in complex networks. II. Percolation properties

TL;DR

This paper analyzes how clustering affects percolation in complex networks, revealing that weak clustering delays and strong clustering promotes the formation of a giant component, with implications confirmed by simulations and real social network data.

Contribution

It provides an analytical method for weak clustering cases and demonstrates how clustering levels influence percolation thresholds and network core structures.

Findings

Weak clustering hinders giant component formation

Strong clustering promotes giant component emergence

Empirical social network data confirms theoretical predictions

Abstract

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the $k$-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.