Random spread on the family of small-world networks

Details Random spread on the family of small-world networks Random spread on the family of small-world networks

2000-04-11

arxiv.org/abs/cond-mat/0004163v1

Physics

Condensed Matter

Statistical Mechanics

RevTeX4 file with 6 figures

Scientific paper

10.1103/PhysRevE.63.041104

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 $p$, 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.

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