{
  "id": "cond-mat/0309436",
  "version": "v2",
  "published": "2003-09-18T16:09:24.000Z",
  "updated": "2004-05-13T12:41:56.000Z",
  "title": "Betweenness Centrality in Large Complex Networks",
  "authors": [
    "Marc Barthelemy"
  ],
  "comment": "6 pages, 5 figures, revised version",
  "journal": "Eur. Phys. Jour. B, vol 38, 163 (2004)",
  "doi": "10.1140/epjb/e2004-00111-4",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent $\\eta$. We find that for trees or networks with a small loop density $\\eta=2$ while a larger density of loops leads to $\\eta<2$. For scale-free networks characterized by an exponent $\\gamma$ which describes the connectivity distribution decay, the BC is also distributed according to a power law with a non universal exponent $\\delta$. We show that this exponent $\\delta$ must satisfy the exact bound $\\delta\\geq (\\gamma+1)/2$. If the scale free network is a tree, then we have the equality $\\delta=(\\gamma+1)/2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-05-13T12:41:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large complex networks",
      "betweenness centrality",
      "power law",
      "small loop density",
      "connectivity distribution decay"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}