{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:O424UNXQNWVUBLG4OXRLW7WGFN","short_pith_number":"pith:O424UNXQ","schema_version":"1.0","canonical_sha256":"7735ca36f06dab40acdc75e2bb7ec62b7f083267f5439d56e91d7e95451f5160","source":{"kind":"arxiv","id":"1908.02967","version":2},"attestation_state":"computed","paper":{"title":"Centrality measures in simplicial complexes: applications of Topological Data Analysis to Network Science","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","physics.soc-ph"],"primary_cat":"math.AT","authors_text":"Daniel Hern\\'andez Serrano, Dar\\'io S\\'anchez G\\'omez","submitted_at":"2019-08-08T08:20:27Z","abstract_excerpt":"Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties of simplicial complex networks centrality measures for simplices need to be proposed. Many of the classical complex networks centralities are based on the degree of a node, so in order to define degree centrality measures for simplices (which would characterise the relevance of a simplicial community in a simplicial network), a different definition of adjacen"},"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":"1908.02967","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-08-08T08:20:27Z","cross_cats_sorted":["math.CO","physics.soc-ph"],"title_canon_sha256":"d76f1e3d573de7d2f8c453c86ed2aeaa057e11bafde2d5e99228b5129cc9c21b","abstract_canon_sha256":"c1c75370e2b730b62e548ad3f7934d34d58cd693579955d2481e594a404ce6d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:55:17.739826Z","signature_b64":"bIXoF2tztarCWzWE+ArG+s1ZjxcrOqLtfXVTbZzRg6zEDMDtv0+KLYJZMfO0gElYor/xqPy5NXQAQNBVS74VAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7735ca36f06dab40acdc75e2bb7ec62b7f083267f5439d56e91d7e95451f5160","last_reissued_at":"2026-07-05T00:55:17.739256Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:55:17.739256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Centrality measures in simplicial complexes: applications of Topological Data Analysis to Network Science","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","physics.soc-ph"],"primary_cat":"math.AT","authors_text":"Daniel Hern\\'andez Serrano, Dar\\'io S\\'anchez G\\'omez","submitted_at":"2019-08-08T08:20:27Z","abstract_excerpt":"Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties of simplicial complex networks centrality measures for simplices need to be proposed. Many of the classical complex networks centralities are based on the degree of a node, so in order to define degree centrality measures for simplices (which would characterise the relevance of a simplicial community in a simplicial network), a different definition of adjacen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02967","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02967/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.02967","created_at":"2026-07-05T00:55:17.739343+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02967v2","created_at":"2026-07-05T00:55:17.739343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02967","created_at":"2026-07-05T00:55:17.739343+00:00"},{"alias_kind":"pith_short_12","alias_value":"O424UNXQNWVU","created_at":"2026-07-05T00:55:17.739343+00:00"},{"alias_kind":"pith_short_16","alias_value":"O424UNXQNWVUBLG4","created_at":"2026-07-05T00:55:17.739343+00:00"},{"alias_kind":"pith_short_8","alias_value":"O424UNXQ","created_at":"2026-07-05T00:55:17.739343+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.02583","citing_title":"Simplicial degree in complex networks. Applications of Topological Data Analysis to Network Science","ref_index":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN","json":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN.json","graph_json":"https://pith.science/api/pith-number/O424UNXQNWVUBLG4OXRLW7WGFN/graph.json","events_json":"https://pith.science/api/pith-number/O424UNXQNWVUBLG4OXRLW7WGFN/events.json","paper":"https://pith.science/paper/O424UNXQ"},"agent_actions":{"view_html":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN","download_json":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN.json","view_paper":"https://pith.science/paper/O424UNXQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02967&json=true","fetch_graph":"https://pith.science/api/pith-number/O424UNXQNWVUBLG4OXRLW7WGFN/graph.json","fetch_events":"https://pith.science/api/pith-number/O424UNXQNWVUBLG4OXRLW7WGFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN/action/storage_attestation","attest_author":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN/action/author_attestation","sign_citation":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN/action/citation_signature","submit_replication":"https://pith.science/pith/O424UNXQNWVUBLG4OXRLW7WGFN/action/replication_record"}},"created_at":"2026-07-05T00:55:17.739343+00:00","updated_at":"2026-07-05T00:55:17.739343+00:00"}