{
  "id": "cond-mat/0403536",
  "version": "v2",
  "published": "2004-03-21T03:09:34.000Z",
  "updated": "2004-11-10T14:32:11.000Z",
  "title": "Statistics of Cycles: How Loopy is your Network?",
  "authors": [
    "Hernan D. Rozenfeld",
    "Joseph E. Kirk",
    "Erik M. Bollt",
    "Daniel ben-Avraham"
  ],
  "comment": "Further work presented and conclusions revised, following referee reports",
  "journal": "J. Phys. A 38, 4589-4595 (2005)",
  "doi": "10.1088/0305-4470/38/21/005",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We study the distribution of cycles of length h in large networks (of size N>>1) and find it to be an excellent ergodic estimator, even in the extreme inhomogeneous case of scale-free networks. The distribution is sharply peaked around a characteristic cycle length, h* ~ N^a. Our results suggest that h* and the exponent a might usefully characterize broad families of networks. In addition to an exact counting of cycles in hierarchical nets, we present a Monte-Carlo sampling algorithm for approximately locating h* and reliably determining a. Our empirical results indicate that for small random scale-free nets of degree exponent g, a=1/(g-1), and a grows as the nets become larger.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-11-10T14:32:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "statistics",
      "small random scale-free nets",
      "excellent ergodic estimator",
      "characteristic cycle length",
      "scale-free networks"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}