{
  "id": "1309.0459",
  "version": "v3",
  "published": "2013-09-02T16:34:07.000Z",
  "updated": "2015-06-28T14:19:49.000Z",
  "title": "Clustering and the hyperbolic geometry of complex networks",
  "authors": [
    "Elisabetta Candellero",
    "Nikolaos Fountoulakis"
  ],
  "comment": "51 pages, 1 figure",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social networks. In this paper, we consider what is called the global clustering coefficient of random graphs on the hyperbolic plane. This model of random graphs was proposed recently by Krioukov et al. as a mathematical model of complex networks, under the fundamental assumption that hyperbolic geometry underlies the structure of these networks. We give a rigorous analysis of clustering and characterize the global clustering coefficient in terms of the parameters of the model. We show how the global clustering coefficient can be tuned by these parameters and we give an explicit formula for this function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-08T21:23:59.000Z",
      "title": "Clustering in random geometric graphs on the hyperbolic plane",
      "abstract": "Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social networks. In this paper, we consider what is called the global clustering coefficient of random graphs on the hyperbolic plane. This model of random graphs was introduced recently by Krioukov et al. as a mathematical model of complex networks, which naturally embeds the (tree-like) hierarchical structure of a complex network into a hyperbolic space. We give a rigorous analysis of clustering and characterize the global clustering coefficient in terms of the parameters of the model. We show that the global clustering coefficient can be tuned by such parameters and we give an explicit formula for this function.",
      "comment": "51 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-06-28T14:19:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C82",
      "05C80",
      "68R05",
      "91D30"
    ],
    "keywords": [
      "random geometric graphs",
      "hyperbolic plane",
      "global clustering coefficient",
      "complex network",
      "random graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0459C"
    }
  }
}