{
  "id": "0711.1452",
  "version": "v1",
  "published": "2007-11-09T12:53:31.000Z",
  "updated": "2007-11-09T12:53:31.000Z",
  "title": "(Un)detectable cluster structure in sparse networks",
  "authors": [
    "Joerg Reichardt",
    "Michele Leone"
  ],
  "comment": "4 Pages, 2 Figures",
  "journal": "Phys. Rev. Lett. 101, 078701 (2008)",
  "doi": "10.1103/PhysRevLett.101.078701",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the problem of recovering a known cluster structure in a sparse network, also known as the planted partitioning problem, by means of statistical mechanics. We find a sharp transition from un-recoverable to recoverable structure as a function of the separation of the clusters. For multivariate data, such transitions have been observed frequently, but always as a function of the number of data points provided, i.e. given a large enough data set, two point clouds can always be recognized as different clusters, as long as their separation is non-zero. In contrast, for the sparse networks studied here, a cluster structure remains undetectable even in an infinitely large network if a critical separation is not exceeded. We give analytic formulas for this critical separation as a function of the degree distribution of the network and calculate the shape of the recoverability-transition. Our findings have implications for unsupervised learning and data-mining in relational data bases and provide bounds on the achievable performance of graph clustering algorithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-09T12:53:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "89.75.Hc",
      "05.50.+q",
      "89.65.-s"
    ],
    "keywords": [
      "sparse network",
      "detectable cluster structure",
      "relational data bases",
      "critical separation",
      "data points"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review Letters",
      "year": 2008,
      "month": "Aug",
      "volume": 101,
      "number": 7,
      "pages": "078701"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvL.101g8701R"
    }
  }
}