Wednesday, July 24, 2013

1307.6186 (Ronan S. Ferreira et al.)

Critical behavior of the contact process on small-world networks    [PDF]

Ronan S. Ferreira, Silvio C. Ferreira
We investigated 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. We have shown that 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 have compared the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and shown that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.
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