{
  "id": "1003.5583",
  "version": "v2",
  "published": "2010-03-29T15:54:03.000Z",
  "updated": "2010-05-26T19:39:18.000Z",
  "title": "Bootstrap Percolation on Complex Networks",
  "authors": [
    "G J Baxter",
    "S N Dorogovtsev",
    "A V Goltsev",
    "J F F Mendes"
  ],
  "comment": "9 pages, 3 figures",
  "journal": "Phys. Rev. E 82, 011103 (2010)",
  "doi": "10.1103/PhysRevE.82.011103",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR",
    "physics.soc-ph"
  ],
  "abstract": "We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any $f>0$ and $p>0$, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-26T19:39:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "64.60.aq",
      "05.10.-a",
      "64.60.ah",
      "05.70.Fh"
    ],
    "keywords": [
      "complex networks",
      "bootstrap percolation",
      "giant active component appears",
      "second transition first appears"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2010,
      "month": "Jul",
      "volume": 82,
      "number": 1,
      "pages": "011103"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvE..82a1103B"
    }
  }
}