{
  "id": "cond-mat/0508435",
  "version": "v1",
  "published": "2005-08-18T18:56:48.000Z",
  "updated": "2005-08-18T18:56:48.000Z",
  "title": "Traversal Times for Random Walks on Small-World Networks",
  "authors": [
    "P. E. Parris",
    "V. M. Kenkre"
  ],
  "comment": "9 pages, 5 figures",
  "doi": "10.1103/PhysRevE.72.056119",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-18T18:56:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walks",
      "simple self-consistent effective medium theory",
      "newman-watts small-world networks",
      "mean traversal time",
      "equal transition rates"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}