{
  "id": "cond-mat/0002076",
  "version": "v1",
  "published": "2000-02-05T16:52:06.000Z",
  "updated": "2000-02-05T16:52:06.000Z",
  "title": "Small-worlds: How and why",
  "authors": [
    "Nisha Mathias",
    "Venkatesh Gopal"
  ],
  "comment": "20 pages, latex, 9 figures",
  "doi": "10.1103/PhysRevE.63.021117",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network architecture. In situations such as neural or transportation networks, where a physical distance between the nodes of the network exists, we study whether the small-world topology arises as a consequence of a tradeoff between maximal connectivity and minimal wiring. Using simulated annealing, we study the properties of a randomly rewired network as the relative tradeoff between wiring and connectivity is varied. When the network seeks to minimize wiring, a regular graph results. At the other extreme, when connectivity is maximized, a near random network is obtained. In the intermediate regime, a small-world network is formed. However, unlike the model of Watts and Strogatz (Nature {\\bf 393}, 440 (1998)), we find an alternate route to small-world behaviour through the formation of hubs, small clusters where one vertex is connected to a large number of neighbours.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-05T16:52:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small-world network",
      "small-world topology arises",
      "regular graph results",
      "large number",
      "maximal connectivity"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}