{
  "id": "1510.08882",
  "version": "v1",
  "published": "2015-10-29T20:22:21.000Z",
  "updated": "2015-10-29T20:22:21.000Z",
  "title": "The diameter of Inhomogeneous random graphs",
  "authors": [
    "Nicolas Fraiman",
    "Dieter Mitsche"
  ],
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "In this paper we study the diameter of Inhomogeneous random graphs $G(n,\\kappa,p)$ that are induced by irreducible kernels $\\kappa$. The kernels we consider act on separable metric spaces and are almost everywhere continuous. We generalize results known for the Erd\\H{o}s-R\\'enyi model $G(n,p)$ for several ranges of $p$. We find upper and lower bounds for the diameter of $G(n,\\kappa,p)$ in terms of the expansion factor and two explicit constants that depend on the behavior of the kernel over partitions of the metric space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-29T20:22:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05C80"
    ],
    "keywords": [
      "inhomogeneous random graphs",
      "explicit constants",
      "expansion factor",
      "lower bounds",
      "separable metric spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}