Percolation and Epidemic Thresholds in Clustered Networks

TL;DR

This paper presents a theoretical analysis of percolation in clustered scale-free networks, showing that clustering does not create a finite epidemic threshold, which has implications for understanding epidemic spread in real-world networks.

Contribution

It introduces a new theoretical approach to percolation in clustered networks and demonstrates that clustering does not induce a finite epidemic threshold in scale-free networks.

Findings

Clustering affects the size and resilience of the giant component.

Clustering does not restore a finite percolation threshold.

Results are supported by numerical simulations.

Abstract

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks extending, thus, this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.