{
  "annotation_id": "59682103-eb3b-4f01-9fdd-611778250e37",
  "date_created": "2026-03-02T18:01:07.152000Z",
  "date_modified": "2026-03-02T18:01:07.152000Z",
  "file_hash": "b09bfc23288bf390bd8643d1f574055f8ffa0fcc4caa87abb6a7257121c636d0",
  "private": false,
  "record": {
    "abstract": "PageRank, the prestige measure for Web pages used by Google, is the\nstationary probability of a peculiar random walk on directed graphs, which\ninterpolates between a pure random walk and a process where all nodes have the\nsame probability of being visited. We give some exact results on the\ndistribution of PageRank in the cases in which the damping factor q approaches\nthe two limit values 0 and 1. When q -\u003e 0 and for several classes of graphs the\ndistribution is a power law with exponent 2, regardless of the in-degree\ndistribution. When q -\u003e 1 it can always be derived from the in-degree\ndistribution of the underlying graph, if the out-degree is the same for all\nnodes.",
    "arxiv_id": "physics/0604203",
    "authors": [
      "Santo Fortunato",
      "Alessandro Flammini"
    ],
    "categories": [
      "physics.soc-ph"
    ],
    "doi": "10.1142/S0218127407018439",
    "title": "Random Walks on Directed Networks: the Case of PageRank",
    "url": "https://arxiv.org/abs/physics/0604203"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6bdf1afa-15cf-49bb-b9d1-4d0ef9a64ae1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}