{
  "id": "1310.7652",
  "version": "v2",
  "published": "2013-10-29T00:34:47.000Z",
  "updated": "2015-04-01T16:56:55.000Z",
  "title": "Connectivity and Giant Component of Stochastic Kronecker Graphs",
  "authors": [
    "Mary Radcliffe",
    "Stephen J. Young"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "cs.DM",
    "cs.SI"
  ],
  "abstract": "Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix k-by-k matrix P with entries in [0,1]. We develop a novel correspondence between the adjacencies in a general stochastic Kronecker graph and the action of a fixed Markov chain. Using this correspondence we are able to generalize the arguments of Horn and Radcliffe on the emergence of the giant component from the case where k = 2 to arbitrary k. We are also able to use this correspondence to completely analyze the connectivity of a general stochastic Kronecker graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-29T00:34:47.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-01T16:56:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C82"
    ],
    "keywords": [
      "giant component",
      "general stochastic kronecker graph",
      "connectivity",
      "fixed matrix k-by-k matrix",
      "complex networks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.7652R"
    }
  }
}