Critical behavior of the contact process on small-world networks

TL;DR

This study examines how clustering affects the critical behavior of the contact process on small-world networks, finding that mean-field theory accurately predicts universality across different clustering levels.

Contribution

It demonstrates that small-world properties ensure mean-field theory's validity for the contact process regardless of clustering degree.

Findings

Critical point predicted by homogeneous cluster-approximation at low clustering

Critical exponents match mean-field predictions for all non-zero clustering

Small heterogeneity slightly shifts the critical point but not other critical quantities

Abstract

We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a homogeneous cluster-approximation for the limit of vanishing clustering (p close to 1). The critical exponents and dimensionless moment ratios of the CP are in agreement with those predicted by the mean-field theory for any p > 0. This independence on the network clustering shows that the small-world property is a sufficient condition for the mean-field theory to correctly predict the universality of the model. Moreover, we compare the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and show that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.