{
  "id": "cond-mat/0509102",
  "version": "v3",
  "published": "2005-09-05T19:21:14.000Z",
  "updated": "2006-02-28T18:05:37.000Z",
  "title": "k-core organization of complex networks",
  "authors": [
    "S. N. Dorogovtsev",
    "A. V. Goltsev",
    "J. F. F. Mendes"
  ],
  "comment": "5 pages, 3 figures",
  "journal": "Phys. Rev. Lett. 96, 040601 (2006)",
  "doi": "10.1103/PhysRevLett.96.040601",
  "categories": [
    "cond-mat.stat-mech",
    "cs.NI",
    "math-ph",
    "math.MP",
    "physics.soc-ph"
  ],
  "abstract": "We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birth points -- the bootstrap percolation thresholds. We show that in networks with a finite mean number z_2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z_2 diverges, the networks contain an infinite sequence of k-cores which are ultra-robust against random damage.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-02-28T18:05:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex networks",
      "k-core organization",
      "hybrid phase transition",
      "finite mean number",
      "bootstrap percolation thresholds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}