{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SPPSVXB36YUY3KVUYW2VYBHLHE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0a8399088347bd0305ea3a127cad632b863c58918c2e5e654f06e9e44a2f63be","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-06-05T12:54:07Z","title_canon_sha256":"72d4d1311e202c7183b116ba54ad0d1edc16209f0399ecf8ea81cc0aeb6fa222"},"schema_version":"1.0","source":{"id":"1806.01664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01664","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01664v2","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01664","created_at":"2026-05-18T00:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"SPPSVXB36YUY","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SPPSVXB36YUY3KVU","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SPPSVXB3","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:ee50fcd355134f6423479c7373b1177b50e6bad55be2ad3e2160a4c9845f8388","target":"graph","created_at":"2026-05-18T00:12:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs. We prove that this distance is reducible, which enables the use of the nearest-neighbor chain to speed up the agglomeration. The output of the algorithm is a regular dendrogram, which reveals the multi-scale structure of the graph. The results are illustrated on both synthetic and real datasets.","authors_text":"Alexandre Hollocou, Alexis Galland, Bertrand Charpentier, Thomas Bonald","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-06-05T12:54:07Z","title":"Hierarchical Graph Clustering using Node Pair Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01664","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d61715a0e599d08147add415774a5d986f12e44268c0b73159788603e787c334","target":"record","created_at":"2026-05-18T00:12:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0a8399088347bd0305ea3a127cad632b863c58918c2e5e654f06e9e44a2f63be","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-06-05T12:54:07Z","title_canon_sha256":"72d4d1311e202c7183b116ba54ad0d1edc16209f0399ecf8ea81cc0aeb6fa222"},"schema_version":"1.0","source":{"id":"1806.01664","kind":"arxiv","version":2}},"canonical_sha256":"93df2adc3bf6298daab4c5b55c04eb391f4a47510dc98a9e662ec59e70b3e554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93df2adc3bf6298daab4c5b55c04eb391f4a47510dc98a9e662ec59e70b3e554","first_computed_at":"2026-05-18T00:12:37.791382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:37.791382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2uoJBSoX0fTRB7Jyp6FfJ+Jj5NBZfg/XNckyGDp/o/jrhzFtfyGVXl8DEZTIdJjXArc36xWtXFeaQWvoLHCjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:37.792208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d61715a0e599d08147add415774a5d986f12e44268c0b73159788603e787c334","sha256:ee50fcd355134f6423479c7373b1177b50e6bad55be2ad3e2160a4c9845f8388"],"state_sha256":"f99c618ecd65ed2ebe6f8ace63478e864234756bba16c185e461f3a0240817a2"}