Random spread on the family of small-world networks
Statistical Mechanics
2009-10-31 v1
Abstract
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the random walk. We introduce an {\em independent step approximation}, which enables us to obtain analytic results for the average access time. We observe a scaling relation for the average access time in the degree of the nodes. The behavior of average access time as a function of , shows striking similarity with that of the {\em characteristic length} of the graph. This observation may have important applications in routing and switching in networks with large number of nodes.
Keywords
Cite
@article{arxiv.cond-mat/0004163,
title = {Random spread on the family of small-world networks},
author = {Sagar A. Pandit and R. E. Amritkar},
journal= {arXiv preprint arXiv:cond-mat/0004163},
year = {2009}
}
Comments
RevTeX4 file with 6 figures