{
  "id": "2003.08411",
  "version": "v1",
  "published": "2020-03-18T18:01:28.000Z",
  "updated": "2020-03-18T18:01:28.000Z",
  "title": "Entropy of the Gibbs state cannot distinguish complex graph models",
  "authors": [
    "Adam Glos",
    "Aleksandra Krawiec",
    "Łukasz Pawela"
  ],
  "categories": [
    "math.PR",
    "quant-ph"
  ],
  "abstract": "In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We show that for a large number of graph models this approach does not distinguish the models asymptotically. We illustrate our analytical results with numerical simulations for Erd\\H{o}s-R\\'enyi, Watts-Strogatz, Barab\\'asi-Albert and Chung-Lu graph models. We conclude saying that, from this perspective, these models are boring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-18T18:01:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distinguish complex graph models",
      "chung-lu graph models",
      "adjacency matrices",
      "large number",
      "gibbs state corresponding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}