We study the mean traversal time tau 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 tau 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.




United States. Defense Advanced Research Projects Agency
National Science Foundation (U.S.)

Keywords and Phrases

Random Processes; Percolation

International Standard Serial Number (ISSN)

1539-3755; 2470-0045

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2004 American Physical Society (APS), All rights reserved.

Publication Date

01 Jan 2004

Included in

Physics Commons