Traversal Times for Random Walks on Small-World Networks
  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. 
P.E. Parris and V.M. Kenkre