Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

Details Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

2004-02-25

arxiv.org/abs/cond-mat/0402622v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 6 figures

Scientific paper

10.1103/PhysRevE.70.016112

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.

Affiliated with

Also associated with

No associations

Rating

Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-484664