Eur. Phys. J. B (2013) 86: 462
https://doi.org/10.1140/epjb/e2013-40534-0

Regular Article

Critical behavior of the contact process on small-world networks

Departamento de Física, Universidade Federal de Viçosa, 36570-000 Viçosa, Minas Gerais, Brazil

^a e-mail: ronan.ferreira@gmail.com

Received: 29 May 2013
Received in final form: 16 August 2013
Published online: 7 November 2013

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 → 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.