{
  "id": "1410.6328",
  "version": "v1",
  "published": "2014-10-23T11:43:19.000Z",
  "updated": "2014-10-23T11:43:19.000Z",
  "title": "Properties of stochastic Kronecker graphs",
  "authors": [
    "Mihyun Kang",
    "Michał Karoński",
    "Christoph Koch",
    "Tamás Makai"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The stochastic Kronecker graph model introduced by Leskovec et al. is a random graph with vertex set $\\mathbb Z_2^n$, where two vertices $u$ and $v$ are connected with probability $\\alpha^{{u}\\cdot{v}}\\gamma^{(1-{u})\\cdot(1-{v})}\\beta^{n-{u}\\cdot{v}-(1-{u})\\cdot(1-{v})}$ independently of the presence or absence of any other edge, for fixed parameters $0<\\alpha,\\beta,\\gamma<1$. They have shown empirically that the degree sequence resembles a power law degree distribution. In this paper we show that the stochastic Kronecker graph a.a.s. does not feature a power law degree distribution for any parameters $0<\\alpha,\\beta,\\gamma<1$. In addition, we analyze the number of subgraphs present in the stochastic Kronecker graph and study the typical neighborhood of any given vertex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-23T11:43:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "power law degree distribution",
      "properties",
      "stochastic kronecker graph model",
      "degree sequence resembles",
      "random graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.6328K"
    }
  }
}