{
  "annotation_id": "6daf5015-bc1b-4ba1-bfac-ffd7a9a86350",
  "date_created": "2026-03-02T18:01:17.751000Z",
  "date_modified": "2026-03-02T18:01:17.751000Z",
  "file_hash": "ceb583ef8d79f9a051807172129e00e5e6afe5e8e7aafd69388826ac741128a1",
  "private": false,
  "record": {
    "abstract": "Random walks on simple graphs in connection with electrical resistor networks\nlead to the definition of Markov chains with transition probability matrix in\nterms of electrical conductances. We extend this definition to an effective\ntransition matrix $P_{ij}$ to account for the probability of going from vertex\n$i$ to any vertex $j$ of the original connected graph $G$. Also, we present an\nalgorithm based on the definition of this effective transition matrix among\nvertices in the network to extract a topological feature related to the manner\ngraph $G$ has been organized. This topological feature corresponds to the\ncommunities in the graph.",
    "arxiv_id": "physics/0703087",
    "authors": [
      "Nelson Augusto Alves"
    ],
    "categories": [
      "physics.soc-ph",
      "cond-mat.stat-mech",
      "physics.data-an"
    ],
    "doi": "10.1103/PhysRevE.76.036101",
    "journal_ref": "Physical Review E 76 (2007) 036101",
    "title": "Unveiling community structures in weighted networks",
    "url": "https://arxiv.org/abs/physics/0703087"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0c074832-94c4-47a6-b6a3-3d7279fbcdbd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}