{
  "id": "1409.4371",
  "version": "v1",
  "published": "2014-09-15T18:39:05.000Z",
  "updated": "2014-09-15T18:39:05.000Z",
  "title": "The strong giant in a random digraph",
  "authors": [
    "Mathew D. Penrose"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a random directed graph on $n$ vertices with independent identically distributed outdegrees with distribution $F$ having mean $\\mu$, and destinations of arcs selected uniformly at random. We show that if $\\mu >1$ then for large $n$ there is very likely to be a unique giant strong component with proportionate size given as the product of two branching process survival probabilities, one with offspring distribution $F$ and the other with Poisson offspring distribution with mean $\\mu$. If $\\mu \\leq 1$ there is very likely to be no giant strong component. We also extend this to allow for $F$ varying with $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-15T18:39:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60J85",
      "92D30"
    ],
    "keywords": [
      "random digraph",
      "strong giant",
      "unique giant strong component",
      "branching process survival probabilities",
      "random directed graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.4371P"
    }
  }
}