Reply to the Comment on the paper "Non-mean-field behavior of the contact process on scale-free networks"

TL;DR

This paper defends the original claim that heterogeneous mean-field theory does not accurately describe the contact process on uncorrelated scale-free networks, using extensive simulations to counter recent criticisms.

Contribution

The authors demonstrate through simulations that mean-field predictions are inaccurate for small degree exponents and clarify the limitations of previous conjectures on finite-size scaling in uncorrelated scale-free networks.

Findings

MF prediction for density decay exponent is incorrect for small degree exponents

Conjecture for finite-size scaling exponent is only approximately valid in unphysical cases

Original conclusion of MF theory's invalidity on real uncorrelated SF networks remains valid

Abstract

The Comment by Ha et al. [cond-mat/0603787] criticizes our recent result [Phys. Rev. Lett. 96, 038701 (2006)] that the contact process (CP) on uncorrelated scale-free (SF) networks does not behave according to heterogeneous mean-field (MF) theory. This claim is based in Gaussian ansatz that reproduces previously reported density fluctuations and numerical simulations for a particular value of the degree exponent $\gamma$ that seem to fit the MF prediction for the density decay exponent $\theta$ and a conjecture of the authors of the comment for the finite-size scaling exponente $\alpha=\beta/ \nu_\perp$. By means of extensive simulations of the CP on random neighbors (RN) SF networks we show that the MF prediction for $\theta4 is incorrect for small degree exponents, while the author's conjecture for $\alpha$ is at best only approximately valid for the unphysical case of uncorrelated networks with cut-off $k_c \sim N^{1/(\gamma-1)}$, which can only be constructed in the RN version of SF networks. Therefore, the main conclusion of our paper [Phys. Rev. Lett. 96, 038701 (2006)], the invalidity of MF theory for real uncorrelated SF networks, remains unchallenged.