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We present high-accuracy quasi-stationary (QS) simulations of the contactprocess in quenched networks, built using the configuration model with bothstructural and natural cutoffs. The critical behavior is analyzed in theframework of the anomalous finite size scaling which was recently shown to holdfor the contact process on annealed networks. It turns out that the quenchedtopology does not qualitatively change the critical behavior, leading only (asexpected) to a shift of the transition point. The anomalous finite size scalingholds with exactly the same exponents of the annealed case, so that we canconclude that heterogeneous mean-field theory works for the contact process onquenched networks, at odds with previous claims. Interestingly, topologicalcorrelations induced by the presence of the natural cutoff do not alter thepicture.

Quasi-stationary simulations of the contact process on quenched networks