{
  "annotation_id": "084ee14a-4463-4214-ab09-f8a2e2c63679",
  "date_created": "2026-03-02T18:00:57.240000Z",
  "date_modified": "2026-03-02T18:00:57.240000Z",
  "file_hash": "569221fbacddbe5b1cf5642dddcd67309f2dc97329be055c127b2be161f9c94c",
  "private": false,
  "record": {
    "abstract": "We find that different geographical structures of networks lead to varied\npercolation thresholds, although these networks may have similar abstract\ntopological structures. Thus, the strategies for enhancing robustness and\nimmunization of a geographical network are proposed. Using the generating\nfunction formalism, we obtain the explicit form of the percolation threshold\n$q_{c}$ for networks containing arbitrary order cycles. For 3-cycles, the\ndependence of $q_c$ on the clustering coefficients is ascertained. The analysis\nsubstantiates the validity of the strategies with an analytical evidence.",
    "arxiv_id": "physics/0503147",
    "authors": [
      "Liang Huang",
      "Lei Yang",
      "Kongqing Yang"
    ],
    "categories": [
      "physics.soc-ph"
    ],
    "doi": "10.1103/PhysRevE.75.036101",
    "journal_ref": "PHYSICAL REVIEW E 75, 036101 (2007)",
    "title": "Enhancing Robustness and Immunization in geographical networks",
    "url": "https://arxiv.org/abs/physics/0503147"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f9554faa-6c2c-4de6-a3e5-55d9e1701b3e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}