{
  "id": "1909.09744",
  "version": "v1",
  "published": "2019-09-21T00:04:50.000Z",
  "updated": "2019-09-21T00:04:50.000Z",
  "title": "PageRank's behavior under degree-degree correlations",
  "authors": [
    "Mariana Olvera-Cravioto"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric, of the rank of a randomly chosen vertex in graphs generated via either a directed configuration model or an inhomogeneous random digraph. The theorem fully characterizes the limiting distribution by expressing it as a random sum of i.i.d.~copies of the attracting endogenous solution to a branching distributional fixed-point equation. In addition, we provide the asymptotic tail behavior of the limit and use it to explain the effect that in-degree/out-degree correlations in the underlying graph can have on the qualitative performance of PageRank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-21T00:04:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60J80",
      "68P20",
      "41A60",
      "37A30",
      "60B10"
    ],
    "keywords": [
      "pageranks behavior",
      "degree-degree correlations",
      "asymptotic tail behavior",
      "googles pagerank algorithm",
      "branching distributional fixed-point equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}