{
  "id": "cond-mat/0205244",
  "version": "v2",
  "published": "2002-05-12T10:34:14.000Z",
  "updated": "2004-10-15T12:07:11.000Z",
  "title": "Simple models of small world networks with directed links",
  "authors": [
    "A. Ramezanpour",
    "V. Karimipour"
  ],
  "comment": "15 pages, 9 figures, published version",
  "journal": "Phys. Rev. E 66, 036128 (2002)",
  "doi": "10.1103/PhysRevE.66.036128",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the effect of directed short and long range connections in a simple model of small world network. Our model is such that we can determine many quantities of interest by an exact analytical method. We calculate the function $V(T)$, defined as the number of sites affected up to time $T$ when a naive spreading process starts in the network. As opposed to shortcuts, the presence of un-favorable bonds has a negative effect on this quantity. Hence the spreading process may not be able to affect all the network. We define and calculate a quantity named the average size of accessible world in our model. The interplay of shortcuts, and un-favorable bonds on the small world properties is studied.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-15T12:07:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small world network",
      "simple model",
      "directed links",
      "long range connections",
      "un-favorable bonds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}