{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZOFSDENEPOLFILA4IOZOTKL5DC","short_pith_number":"pith:ZOFSDENE","schema_version":"1.0","canonical_sha256":"cb8b2191a47b96542c1c43b2e9a97d1891764d0718cd8d23fef7a9daa1450585","source":{"kind":"arxiv","id":"1410.7357","version":3},"attestation_state":"computed","paper":{"title":"Statistical models for cores decomposition of an undirected random graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph","stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Dane Wilburne, Despina Stasi, Michael J. Pelsmajer, Sonja Petrovi\\'c, Vishesh Karwa","submitted_at":"2014-10-27T19:08:50Z","abstract_excerpt":"The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core decomposition as a tool to model random graphs. We propose using the shell distribution vector, a way of summarizing the decomposition, as a sufficient statistic for a family of exponential random graph models. We study the properties and behavior of the model family, implement a Markov chain Monte Carlo algorithm for simulating graphs from the model, implemen"},"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":"1410.7357","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-10-27T19:08:50Z","cross_cats_sorted":["cs.SI","physics.soc-ph","stat.CO","stat.TH"],"title_canon_sha256":"89722953f350f4793c34d877f5ff70abf4f68422a41761fbc2a40d815b6f0039","abstract_canon_sha256":"f8c9911b1a4b14a9522f324644522e1059ec424605efc91e1273a4a8968e4ba4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:36.272514Z","signature_b64":"kF6lhsMCXkCJUsnhyVAuPMw+1YGy6hKM9F/WnqYXRjrjoFVMX++75Vur5Fk3uKkwlfxbMrSm7/IYqvsCjX5SBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb8b2191a47b96542c1c43b2e9a97d1891764d0718cd8d23fef7a9daa1450585","last_reissued_at":"2026-05-18T00:56:36.271824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:36.271824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Statistical models for cores decomposition of an undirected random graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph","stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Dane Wilburne, Despina Stasi, Michael J. Pelsmajer, Sonja Petrovi\\'c, Vishesh Karwa","submitted_at":"2014-10-27T19:08:50Z","abstract_excerpt":"The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core decomposition as a tool to model random graphs. We propose using the shell distribution vector, a way of summarizing the decomposition, as a sufficient statistic for a family of exponential random graph models. We study the properties and behavior of the model family, implement a Markov chain Monte Carlo algorithm for simulating graphs from the model, implemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7357","kind":"arxiv","version":3},"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":"1410.7357","created_at":"2026-05-18T00:56:36.271931+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.7357v3","created_at":"2026-05-18T00:56:36.271931+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7357","created_at":"2026-05-18T00:56:36.271931+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOFSDENEPOLF","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOFSDENEPOLFILA4","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOFSDENE","created_at":"2026-05-18T12:28:59.999130+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/ZOFSDENEPOLFILA4IOZOTKL5DC","json":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC.json","graph_json":"https://pith.science/api/pith-number/ZOFSDENEPOLFILA4IOZOTKL5DC/graph.json","events_json":"https://pith.science/api/pith-number/ZOFSDENEPOLFILA4IOZOTKL5DC/events.json","paper":"https://pith.science/paper/ZOFSDENE"},"agent_actions":{"view_html":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC","download_json":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC.json","view_paper":"https://pith.science/paper/ZOFSDENE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.7357&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOFSDENEPOLFILA4IOZOTKL5DC/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOFSDENEPOLFILA4IOZOTKL5DC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC/action/storage_attestation","attest_author":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC/action/author_attestation","sign_citation":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC/action/citation_signature","submit_replication":"https://pith.science/pith/ZOFSDENEPOLFILA4IOZOTKL5DC/action/replication_record"}},"created_at":"2026-05-18T00:56:36.271931+00:00","updated_at":"2026-05-18T00:56:36.271931+00:00"}