{
  "id": "1211.5937",
  "version": "v3",
  "published": "2012-11-26T12:50:43.000Z",
  "updated": "2014-09-02T09:56:14.000Z",
  "title": "Comparing the reliability of networks by spectral analysis",
  "authors": [
    "Zitao Wang",
    "Kwok Yip Szeto"
  ],
  "comment": "7 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cs.SI",
    "physics.soc-ph"
  ],
  "abstract": "We provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with the same connectance and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically for the IEEE57, the Erd\\H{o}s-R\\'enyi, and the Small-World networks.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-26T22:34:54.000Z",
      "title": "Comparing the stability and reliability of networks by spectral analysis",
      "abstract": "We provide a method for the ranking of the reliability of two networks with the same connectivity, without using the theory of signature. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with same connectivity and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are then generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically in the IEEE57, the Erd\\H{o}s-R\\'{e}nyi, and the Small-World networks.",
      "comment": "6 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-02T09:56:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral analysis",
      "reliability",
      "connectivity",
      "eigenvalue gaps",
      "degree distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5937W"
    }
  }
}