{
  "id": "1111.1500",
  "version": "v1",
  "published": "2011-11-07T07:46:37.000Z",
  "updated": "2011-11-07T07:46:37.000Z",
  "title": "Mean first-passage time for random walks on undirected networks",
  "authors": [
    "Zhongzhi Zhang",
    "Alafate Julaiti",
    "Baoyu Hou",
    "Hongjuan Zhang",
    "Guanrong Chen"
  ],
  "comment": "7 pages, no figures; definitive version published in European Physical Journal B",
  "journal": "Eur. Phys. J. B 84, 691-697 (2011)",
  "doi": "10.1140/epjb/e2011-20834-1",
  "categories": [
    "cond-mat.stat-mech",
    "physics.class-ph"
  ],
  "abstract": "In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\\sim d^{-\\gamma}$, the scaling of the lower bound is $N^{1-1/\\gamma}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-07T07:46:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean first-passage time",
      "random walks",
      "lower bound",
      "complex networks",
      "general undirected network"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "European Physical Journal B",
      "year": 2011,
      "month": "Dec",
      "volume": 84,
      "number": 4,
      "pages": 691
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011EPJB...84..691Z"
    }
  }
}