Percolation in clustered networks

TL;DR

This paper investigates how clustering in social networks affects percolation and epidemic thresholds, revealing that clustering reduces component sizes and raises the epidemic threshold, thus impacting disease spread dynamics.

Contribution

It introduces new classes of random clustered and unclustered networks with preferential mixing and analytically compares their percolation properties.

Findings

Clustering reduces the size of connected components.

Clustering increases the epidemic threshold.

Preferential mixing influences percolation behavior.

Abstract

The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease dynamics. A number of authors have studied clustered networks, but the networks often contain preferential mixing between high degree nodes. We introduce a class of random clustered networks and another class of random unclustered networks with the same preferential mixing. We analytically show that percolation in the clustered networks reduces the component sizes and increases the epidemic threshold compared to the unclustered networks.