Traversal Times for Random Walks on Small-World Networks

Details Traversal Times for Random Walks on Small-World Networks Traversal Times for Random Walks on Small-World Networks

2005-08-18

arxiv.org/abs/cond-mat/0508435v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 5 figures

Scientific paper

10.1103/PhysRevE.72.056119

We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world connections. When f >> F, the mean time to traverse the network exhibits a transition associated with percolation of the random graph (i.e., small-world) part of the network, and a collapse of the data onto a universal curve. This transition was not observed in earlier studies in which equal transition rates were assumed for all allowed steps. We develop a simple self-consistent effective medium theory and show that it gives a quantitatively correct description of the traversal time in all parameter regimes except the immediate neighborhood of the transition, as is characteristic of most effective medium theories.

Affiliated with

Also associated with

No associations

Rating

Traversal Times for Random Walks on Small-World 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 Traversal Times for Random Walks on Small-World Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Traversal Times for Random Walks on Small-World Networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-119839