{
  "id": "cond-mat/0203278",
  "version": "v2",
  "published": "2002-03-13T14:38:33.000Z",
  "updated": "2002-05-08T15:51:25.000Z",
  "title": "Shortest paths and load scaling in scale-free trees",
  "authors": [
    "Gabor Szabo",
    "Mikko Alava",
    "Janos Kertesz"
  ],
  "comment": "8 pages, 8 figures; v2: load calculations extended",
  "journal": "Phys. Rev. E 66, 026101 (2002)",
  "doi": "10.1103/PhysRevE.66.026101",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabasi-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows a demonstration of why the distribution approaches a Gaussian in the limit of N large. The load (betweenness), the number of shortest distance paths passing through any node, is discussed in the tree presentation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-05-08T15:51:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scale-free trees",
      "shortest paths",
      "load scaling",
      "probability distribution function",
      "average node-to-node distance"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}