Random spreading phenomena in annealed small world networks
Abstract
We study the simple random walk dynamics on an annealed version of a Small-World Network (SWN) consisting of nodes. This is done by calculating the mean number of distinct sites visited S(n) and the return probability as a function of the time . is a key quantity both from the statistical physics point of view and especially for characterizing the efficiency of the network connectedness. Our results for this quantity shows features similar to the SWN with quenched disorder, but with a crossover time that goes inversely proportianal to the probability of making a long range jump instead of being proportional to as in quenched case. We have also carried out simulations on a modified annealed model where the crossover time goes as due to specific time dependent transition probabilities and we present an approximate self-consistent solution to it.
Cite
@article{arxiv.cond-mat/0110365,
title = {Random spreading phenomena in annealed small world networks},
author = {Jani Lahtinen and János Kertész and Kimmo Kaski},
journal= {arXiv preprint arXiv:cond-mat/0110365},
year = {2009}
}