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Reply to the Comment on the paper "Non-mean-field behavior of the contact process on scale-free networks" | | C. Castellano
; R. Pastor-Satorras
; | | Date: |
12 Jan 2007 | | Subject: | Disordered Systems and Neural Networks | | 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 $ heta$ and a conjecture of the authors of the comment for the finite-size scaling exponente $alpha=eta/
u_perp$. By means of extensive simulations of the CP on random neighbors (RN) SF networks we show that the MF prediction for $ heta4 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. | | Source: | arXiv, cond-mat/0701275 | | Services: | Forum | Review | PDF | Favorites | |
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