{
  "id": "1810.06495",
  "version": "v1",
  "published": "2018-10-15T16:14:00.000Z",
  "updated": "2018-10-15T16:14:00.000Z",
  "title": "Generalised hypergeometric ensembles of random graphs: the configuration model as an urn problem",
  "authors": [
    "Giona Casiraghi",
    "Vahan Nanumyan"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.PR",
    "cs.SI",
    "physics.data-an",
    "physics.soc-ph"
  ],
  "abstract": "We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation of the well-known configuration model in terms of an urn problem. Second, GHypEG allows to incorporate arbitrary tendencies to connect different vertex pairs. Third, we present the closed-form expressions of the associated probability distribution ensures the analytical tractability of our formulation. This is in stark contrast with the previous state-of-the-art, which is to implement the configuration model by means of computationally expensive procedures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-15T16:14:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60C05"
    ],
    "keywords": [
      "generalised hypergeometric ensemble",
      "urn problem",
      "random graph models",
      "random graph theory",
      "well-known configuration model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}