{
  "id": "0710.3319",
  "version": "v3",
  "published": "2007-10-17T15:25:03.000Z",
  "updated": "2010-05-08T20:36:48.000Z",
  "title": "Correlations in connected random graphs",
  "authors": [
    "Piotr Bialas",
    "Andrzej K. Oleś"
  ],
  "comment": "Synchronized with the published version; 11 pages and 11 figures.",
  "journal": "P. Bialas and A. K. Oles, Phys. Rev. E 77, 036124 (2008).",
  "doi": "10.1103/PhysRevE.77.036124",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.other"
  ],
  "abstract": "We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated and derive analytic formulas for the joint nearest-neighbor degree probability distribution. Using those results we describe the correlations in maximal entropy connected random graphs. We show that connected graphs are disassortative and that correlations are strongly related to the presence of one-degree nodes (leaves). We propose an efficient algorithm for generating connected random graphs. We illustrate our results with several examples.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-05-08T20:36:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "89.75.Hc",
      "05.10.-a",
      "05.90.+m"
    ],
    "keywords": [
      "correlations",
      "joint nearest-neighbor degree probability distribution",
      "giant connected component",
      "maximal entropy connected random graphs",
      "arbitrary degree distribution"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2008,
      "month": "Mar",
      "volume": 77,
      "number": 3,
      "pages": "036124"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvE..77c6124B"
    }
  }
}