{
  "id": "1210.6259",
  "version": "v1",
  "published": "2012-10-23T15:03:13.000Z",
  "updated": "2012-10-23T15:03:13.000Z",
  "title": "Connectivity of inhomogeneous random graphs",
  "authors": [
    "Luc Devroye",
    "Nicolas Fraiman"
  ],
  "comment": "13 pages. To appear in Random Structures and Algorithms",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a separable metric space, and let their indices form the vertex set of a graph. An edge (i,j) is added with probability min(1, \\K(X_i,X_j) log n/n), where \\K \\ge 0 is a fixed kernel. We show that, under reasonably weak assumptions, the connectivity threshold of the model can be determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-23T15:03:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60C05"
    ],
    "keywords": [
      "inhomogeneous random graphs",
      "log n/n",
      "connectivity threshold",
      "independent points",
      "intermediate density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6259D"
    }
  }
}