Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks
Abstract
In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.
Keywords
Cite
@article{arxiv.cond-mat/0402622,
title = {Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks},
author = {F. Jasch and C. von Ferber and A. Blumen},
journal= {arXiv preprint arXiv:cond-mat/0402622},
year = {2016}
}
Comments
9 pages, 6 figures