{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:SUOKEFSXMTXYTCYIDRQXL4ESJS","short_pith_number":"pith:SUOKEFSX","schema_version":"1.0","canonical_sha256":"951ca2165764ef898b081c6175f0924c8ffb52f9033415f16390cda3b88f4970","source":{"kind":"arxiv","id":"1211.2651","version":2},"attestation_state":"computed","paper":{"title":"Correlation dimension of complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Jesus Gomez-Garde\\~nes, Lucas Lacasa","submitted_at":"2012-11-08T16:45:27Z","abstract_excerpt":"We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only reli"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.2651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-11-08T16:45:27Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"5b484b76a8224e27324da67b098113b4ca1de886235dc2a95ea6a9c462ac6964","abstract_canon_sha256":"12e84d1f14a4ff1986b1e0fc151454be2f96228270826be1cdc0063db96287c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:16.725425Z","signature_b64":"ormYmdmclv4h7AG9/WOMoXA70Lob3QlZqqiqBx41sAbyIv8nwoizNgl5K8kdenQAtwDB2wfvWnRNnWkmYmhSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"951ca2165764ef898b081c6175f0924c8ffb52f9033415f16390cda3b88f4970","last_reissued_at":"2026-05-18T01:53:16.724984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:16.724984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlation dimension of complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Jesus Gomez-Garde\\~nes, Lucas Lacasa","submitted_at":"2012-11-08T16:45:27Z","abstract_excerpt":"We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only reli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2651","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.2651","created_at":"2026-05-18T01:53:16.725049+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2651v2","created_at":"2026-05-18T01:53:16.725049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2651","created_at":"2026-05-18T01:53:16.725049+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUOKEFSXMTXY","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUOKEFSXMTXYTCYI","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUOKEFSX","created_at":"2026-05-18T12:27:23.164592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS","json":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS.json","graph_json":"https://pith.science/api/pith-number/SUOKEFSXMTXYTCYIDRQXL4ESJS/graph.json","events_json":"https://pith.science/api/pith-number/SUOKEFSXMTXYTCYIDRQXL4ESJS/events.json","paper":"https://pith.science/paper/SUOKEFSX"},"agent_actions":{"view_html":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS","download_json":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS.json","view_paper":"https://pith.science/paper/SUOKEFSX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2651&json=true","fetch_graph":"https://pith.science/api/pith-number/SUOKEFSXMTXYTCYIDRQXL4ESJS/graph.json","fetch_events":"https://pith.science/api/pith-number/SUOKEFSXMTXYTCYIDRQXL4ESJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS/action/storage_attestation","attest_author":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS/action/author_attestation","sign_citation":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS/action/citation_signature","submit_replication":"https://pith.science/pith/SUOKEFSXMTXYTCYIDRQXL4ESJS/action/replication_record"}},"created_at":"2026-05-18T01:53:16.725049+00:00","updated_at":"2026-05-18T01:53:16.725049+00:00"}