{
  "id": "math/0606414",
  "version": "v1",
  "published": "2006-06-17T01:36:37.000Z",
  "updated": "2006-06-17T01:36:37.000Z",
  "title": "The Rank of Random Graphs",
  "authors": [
    "Kevin P. Costello",
    "Van H. Vu"
  ],
  "comment": "19 pages, no figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We show that almost surely the rank of the adjacency matrix of the Erd\\\"os-R\\'enyi random graph $G(n,p)$ equals the number of non-isolated vertices for any $c\\ln n/n<p<1/2$, where $c$ is an arbitrary positive constant larger than 1/2. In particular, the giant component (a.s.) has full rank in this range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-17T01:36:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52"
    ],
    "keywords": [
      "random graph",
      "arbitrary positive constant larger",
      "full rank",
      "adjacency matrix",
      "giant component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6414C"
    }
  }
}