{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5ZFVPGTSIEPX7AGP6GSQ7FG23M","short_pith_number":"pith:5ZFVPGTS","schema_version":"1.0","canonical_sha256":"ee4b579a72411f7f80cff1a50f94dadb2b67467b305d3518cfed1d69a3eee1f6","source":{"kind":"arxiv","id":"1611.06135","version":1},"attestation_state":"computed","paper":{"title":"Large Values of the Clustering Coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Irene Heinrich, Michael Gentner, Simon J\\\"ager","submitted_at":"2016-11-18T15:58:10Z","abstract_excerpt":"A prominent parameter in the context of network analysis, originally proposed by Watts and Strogatz (Collective dynamics of `small-world' networks, Nature 393 (1998) 440-442), is the clustering coefficient of a graph $G$. It is defined as the arithmetic mean of the clustering coefficients of its vertices, where the clustering coefficient of a vertex $u$ of $G$ is the relative density $m(G[N_G(u)])/{d_G(u)\\choose 2}$ of its neighborhood if $d_G(u)$ is at least $2$, and $0$ otherwise. It is unknown which graphs maximize the clustering coefficient among all connected graphs of given order and siz"},"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":"1611.06135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T15:58:10Z","cross_cats_sorted":[],"title_canon_sha256":"8dc2ea9eefa6d4e028a27cdec0e1fe94e5cb979091b555435f650bb29d05c534","abstract_canon_sha256":"977df609274205658b9883c8f2fb3301ba76bfc45d87391365ad0188555c16e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:42.993609Z","signature_b64":"DRQZnOjUe9Vk5f7c81GlOr1Ir8RXBzAehJYoGNYg16Kxcg1cfaW+iskaJeapxOnqfuSn8NIcwejbNZUnv14jAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee4b579a72411f7f80cff1a50f94dadb2b67467b305d3518cfed1d69a3eee1f6","last_reissued_at":"2026-05-18T00:57:42.993199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:42.993199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large Values of the Clustering Coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Irene Heinrich, Michael Gentner, Simon J\\\"ager","submitted_at":"2016-11-18T15:58:10Z","abstract_excerpt":"A prominent parameter in the context of network analysis, originally proposed by Watts and Strogatz (Collective dynamics of `small-world' networks, Nature 393 (1998) 440-442), is the clustering coefficient of a graph $G$. It is defined as the arithmetic mean of the clustering coefficients of its vertices, where the clustering coefficient of a vertex $u$ of $G$ is the relative density $m(G[N_G(u)])/{d_G(u)\\choose 2}$ of its neighborhood if $d_G(u)$ is at least $2$, and $0$ otherwise. It is unknown which graphs maximize the clustering coefficient among all connected graphs of given order and siz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06135","kind":"arxiv","version":1},"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":"1611.06135","created_at":"2026-05-18T00:57:42.993260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.06135v1","created_at":"2026-05-18T00:57:42.993260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06135","created_at":"2026-05-18T00:57:42.993260+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZFVPGTSIEPX","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZFVPGTSIEPX7AGP","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZFVPGTS","created_at":"2026-05-18T12:30:01.593930+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/5ZFVPGTSIEPX7AGP6GSQ7FG23M","json":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M.json","graph_json":"https://pith.science/api/pith-number/5ZFVPGTSIEPX7AGP6GSQ7FG23M/graph.json","events_json":"https://pith.science/api/pith-number/5ZFVPGTSIEPX7AGP6GSQ7FG23M/events.json","paper":"https://pith.science/paper/5ZFVPGTS"},"agent_actions":{"view_html":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M","download_json":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M.json","view_paper":"https://pith.science/paper/5ZFVPGTS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.06135&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZFVPGTSIEPX7AGP6GSQ7FG23M/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZFVPGTSIEPX7AGP6GSQ7FG23M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M/action/storage_attestation","attest_author":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M/action/author_attestation","sign_citation":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M/action/citation_signature","submit_replication":"https://pith.science/pith/5ZFVPGTSIEPX7AGP6GSQ7FG23M/action/replication_record"}},"created_at":"2026-05-18T00:57:42.993260+00:00","updated_at":"2026-05-18T00:57:42.993260+00:00"}