{
  "id": "cond-mat/0403453",
  "version": "v1",
  "published": "2004-03-18T03:19:24.000Z",
  "updated": "2004-03-18T03:19:24.000Z",
  "title": "Unicyclic Components in Random Graphs",
  "authors": [
    "E. Ben-Naim",
    "P. L. Krapivsky"
  ],
  "comment": "4 pages, 2 figures",
  "journal": "J. Phys. A 37, L189 (2004)",
  "doi": "10.1088/0305-4470/37/18/L01",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "cs.DS",
    "math.PR"
  ],
  "abstract": "The distribution of unicyclic components in a random graph is obtained analytically. The number of unicyclic components of a given size approaches a self-similar form in the vicinity of the gelation transition. At the gelation point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a result, the total number of unicyclic components grows logarithmically with the system size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-18T03:19:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graph",
      "self-similar form",
      "gelation transition",
      "gelation point",
      "total number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}