{
  "id": "1407.8421",
  "version": "v2",
  "published": "2014-07-31T14:05:44.000Z",
  "updated": "2015-05-13T10:47:41.000Z",
  "title": "Preferential attachment with choice",
  "authors": [
    "John Haslegrave",
    "Jonathan Jordan"
  ],
  "comment": "17 pages, 1 figure. Accepted for publication in Random Structures and Algorithms",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices according to a preferential rule and connects to the vertex in the selection with the $s$th highest degree. For meek choice, where $s>1$, we show that both double exponential decay of the degree distribution and condensation-like behaviour are possible, and provide a criterion to distinguish between them. For greedy choice, where $s=1$, we confirm that the degree distribution asympotically follows a power law with logarithmic correction when $r=2$ and shows condensation-like behaviour when $r>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-31T14:05:44.000Z",
      "comment": "14 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-13T10:47:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C82"
    ],
    "keywords": [
      "degree distribution",
      "preferential attachment random graph models",
      "th highest degree",
      "condensation-like behaviour",
      "preferential rule"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.8421H"
    }
  }
}