{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FXYEGBPAGS3YGAJ6YCJ5AR7PIY","short_pith_number":"pith:FXYEGBPA","schema_version":"1.0","canonical_sha256":"2df04305e034b783013ec093d047ef463cbc9b33c7e0167cf27d67040b6cae4d","source":{"kind":"arxiv","id":"1709.09477","version":1},"attestation_state":"computed","paper":{"title":"Random Overlapping Communities: Approximating Motif Densities of Large Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math.CO"],"primary_cat":"cs.DM","authors_text":"Samantha Petti, Santosh Vempala","submitted_at":"2017-09-27T12:50:06Z","abstract_excerpt":"A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs capture power law degree distributions (Barab\\'asi-Albert) and small-world properties (Watts-Strogatz), but only limited clustering behavior. We introduce a generalization of the classical Erd\\H{o}s-R\\'enyi model of random graphs which provably achieves a wide range of desired clustering coefficient, triangle-to-edge and four-cycle-to-edge ratios for any given g"},"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":"1709.09477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-09-27T12:50:06Z","cross_cats_sorted":["cs.SI","math.CO"],"title_canon_sha256":"8d815145aed6535595d707afac860040584af66f0f798989926ceb1ff9691796","abstract_canon_sha256":"aa1ba12dba0820e0512d2fce8d5d0decfc3cac012d456565e66052c41cf30e97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:11.632737Z","signature_b64":"bmI5uwm6ioD4xr4fdQR3hVmz2BS4I3ixXfUX5ONIqtDq7XMfCSPXDPGc5uNXvPKRACfaDULykyFT8lgZdTlgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2df04305e034b783013ec093d047ef463cbc9b33c7e0167cf27d67040b6cae4d","last_reissued_at":"2026-05-18T00:34:11.632066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:11.632066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Overlapping Communities: Approximating Motif Densities of Large Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math.CO"],"primary_cat":"cs.DM","authors_text":"Samantha Petti, Santosh Vempala","submitted_at":"2017-09-27T12:50:06Z","abstract_excerpt":"A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs capture power law degree distributions (Barab\\'asi-Albert) and small-world properties (Watts-Strogatz), but only limited clustering behavior. We introduce a generalization of the classical Erd\\H{o}s-R\\'enyi model of random graphs which provably achieves a wide range of desired clustering coefficient, triangle-to-edge and four-cycle-to-edge ratios for any given g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09477","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":"1709.09477","created_at":"2026-05-18T00:34:11.632163+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.09477v1","created_at":"2026-05-18T00:34:11.632163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09477","created_at":"2026-05-18T00:34:11.632163+00:00"},{"alias_kind":"pith_short_12","alias_value":"FXYEGBPAGS3Y","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FXYEGBPAGS3YGAJ6","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FXYEGBPA","created_at":"2026-05-18T12:31:15.632608+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/FXYEGBPAGS3YGAJ6YCJ5AR7PIY","json":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY.json","graph_json":"https://pith.science/api/pith-number/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/graph.json","events_json":"https://pith.science/api/pith-number/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/events.json","paper":"https://pith.science/paper/FXYEGBPA"},"agent_actions":{"view_html":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY","download_json":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY.json","view_paper":"https://pith.science/paper/FXYEGBPA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.09477&json=true","fetch_graph":"https://pith.science/api/pith-number/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/graph.json","fetch_events":"https://pith.science/api/pith-number/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/action/storage_attestation","attest_author":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/action/author_attestation","sign_citation":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/action/citation_signature","submit_replication":"https://pith.science/pith/FXYEGBPAGS3YGAJ6YCJ5AR7PIY/action/replication_record"}},"created_at":"2026-05-18T00:34:11.632163+00:00","updated_at":"2026-05-18T00:34:11.632163+00:00"}