{
  "annotation_id": "143de029-9a47-4c0a-9ff5-3a01983f2134",
  "date_created": "2026-03-02T18:01:04.120000Z",
  "date_modified": "2026-03-02T18:01:04.120000Z",
  "file_hash": "27719ded623094174a26df5544b93685ec1283033cce261578621b50cec693e8",
  "private": false,
  "record": {
    "abstract": "We have proposed two new dynamic networks where two node are swapped each\nother, and showed that the both networks behave as a small world like in the\naverage path length but can not make any effective discussions on the\nclustering coefficient because of the topological invariant properties of the\nnetworks. In this article we introduce a new index, \"hamming coefficient\" or\n\"multiplicity\", that can act well for these dynamic networks. The hamming\ncoefficient or multiplicity is shown essentially to behave as the clustering\ncoefficient in the small world network proposed by Watts and\nStrogatz\\cite{Watt1}. By evaluating the new index, we uncover another\nproperties of the two networks.",
    "arxiv_id": "physics/0601068",
    "authors": [
      "Norihito Toyota"
    ],
    "categories": [
      "physics.soc-ph"
    ],
    "title": "The Analyses of Node Swapping Networks by New Graph Index",
    "url": "https://arxiv.org/abs/physics/0601068"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2066e518-af84-44ed-8151-6464a6ab6aca",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}