{
  "id": "0707.0560",
  "version": "v2",
  "published": "2007-07-04T09:03:15.000Z",
  "updated": "2007-08-14T06:35:33.000Z",
  "title": "Percolation and Loop Statistics in Complex Networks",
  "authors": [
    "Jae Dong Noh"
  ],
  "comment": "4 pages and 2 figures; A major revision has been made",
  "journal": "Eur. Phys. J. B 66, 251 (2008)",
  "doi": "10.1140/epjb/e2008-00401-9",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a genuine structural correlation is an essential ingredient in characterizing networks. As a signature of the correlation we investigate a scaling behavior in $M_N(h)$, the number of finite loops of size $h$, with respect to a network size $N$. We find that networks, whose degree distributions are not too broad, fall into two classes exhibiting $M_N(h)\\sim ({constant})$ and $M_N(h) \\sim (\\ln N)^\\psi$, respectively. This classification coincides with the one according to the percolation critical phenomena.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-14T06:35:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "89.75.Hc",
      "05.10.-a",
      "05.50.+q"
    ],
    "keywords": [
      "loop statistics",
      "degree distribution",
      "complex networks display",
      "diverse percolation critical phenomena",
      "genuine structural correlation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "European Physical Journal B",
      "year": 2008,
      "month": "Nov",
      "volume": 66,
      "number": 2,
      "pages": 251
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008EPJB...66..251N"
    }
  }
}