{
  "id": "cond-mat/0205589",
  "version": "v2",
  "published": "2002-05-28T12:03:41.000Z",
  "updated": "2002-10-20T19:07:01.000Z",
  "title": "Correlated random networks",
  "authors": [
    "Johannes Berg",
    "Michael Lässig"
  ],
  "comment": "4 pages Revex",
  "journal": "Phys. Rev. Lett. 89 (22),228701 (2002)",
  "doi": "10.1103/PhysRevLett.89.228701",
  "categories": [
    "cond-mat.stat-mech",
    "q-bio.MN"
  ],
  "abstract": "We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\\sum_{\\c} \\exp {[}-\\beta \\H(\\c) {]}$. The simplest cases are uncorrelated random networks such as the well-known Erd\\\"os-R\\'eny graphs. Here we study more general interactions $\\H(\\c)$ which lead to {\\em correlations}, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in {\\em optimized} networks described by partition functions in the limit $\\beta \\to \\infty$. They are argued to be a crucial signature of evolutionary design in biological networks.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-10-20T19:07:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partition function",
      "relevant statistical ensembles",
      "simplest cases",
      "adjacency matrix",
      "uncorrelated random networks"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}