{
  "id": "2003.04965",
  "version": "v1",
  "published": "2020-03-10T20:53:59.000Z",
  "updated": "2020-03-10T20:53:59.000Z",
  "title": "The diameter of the directed configuration model",
  "authors": [
    "Xing Shi Cai",
    "Guillem Perarnau"
  ],
  "comment": "33 pages, 2 figures",
  "categories": [
    "math.PR",
    "cs.DM"
  ],
  "abstract": "We show that the diameter of the directed configuration model with $n$ vertices rescaled by $\\log n$ converges in probability to a constant. Our assumptions are the convergence of the in- and out-degree of a uniform random vertex in distribution, first and second moment. Our result extends previous results on the diameter of the model and applies to many other random directed graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-10T20:53:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "G.3"
    ],
    "keywords": [
      "directed configuration model",
      "uniform random vertex",
      "result extends",
      "second moment",
      "random directed graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}