{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TKAPLOVRLORDYR77YYQZM543PS","short_pith_number":"pith:TKAPLOVR","schema_version":"1.0","canonical_sha256":"9a80f5bab15ba23c47ffc62196779b7c947ddbf8dc35cc89351a0a7cc3098dfb","source":{"kind":"arxiv","id":"1508.04388","version":2},"attestation_state":"computed","paper":{"title":"Hierarchical mutual information for the comparison of hierarchical community structures in complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","physics.bio-ph"],"primary_cat":"physics.soc-ph","authors_text":"Claudio Juan Tessone, Guido Caldarelli, Juan Ignacio Perotti","submitted_at":"2015-08-18T17:21:25Z","abstract_excerpt":"The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the {\\it hierarchical mutual information}, which is a generalization of the traditional mutual information, and allows to comp"},"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":"1508.04388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-08-18T17:21:25Z","cross_cats_sorted":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","physics.bio-ph"],"title_canon_sha256":"171fe960c859159588fa99fdb18610fa40bc9555288f33f321336f3e7fc91060","abstract_canon_sha256":"16e1531ae4fdfc7f3dfaf139975892157192b5aa5270f1d7b7a6652b4336b3ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:16.249001Z","signature_b64":"ZODCV6cZQjuahT/5e+jjcUe59plAEUPLc9mwWejlx3X0kAMznirzM5Rc7VtcCA4ucGFlwyYVdBtFCJ9lfgbBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a80f5bab15ba23c47ffc62196779b7c947ddbf8dc35cc89351a0a7cc3098dfb","last_reissued_at":"2026-05-18T01:23:16.248215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:16.248215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical mutual information for the comparison of hierarchical community structures in complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","physics.bio-ph"],"primary_cat":"physics.soc-ph","authors_text":"Claudio Juan Tessone, Guido Caldarelli, Juan Ignacio Perotti","submitted_at":"2015-08-18T17:21:25Z","abstract_excerpt":"The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the {\\it hierarchical mutual information}, which is a generalization of the traditional mutual information, and allows to comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04388","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":""},"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":"1508.04388","created_at":"2026-05-18T01:23:16.248368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04388v2","created_at":"2026-05-18T01:23:16.248368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04388","created_at":"2026-05-18T01:23:16.248368+00:00"},{"alias_kind":"pith_short_12","alias_value":"TKAPLOVRLORD","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TKAPLOVRLORDYR77","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TKAPLOVR","created_at":"2026-05-18T12:29:42.218222+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/TKAPLOVRLORDYR77YYQZM543PS","json":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS.json","graph_json":"https://pith.science/api/pith-number/TKAPLOVRLORDYR77YYQZM543PS/graph.json","events_json":"https://pith.science/api/pith-number/TKAPLOVRLORDYR77YYQZM543PS/events.json","paper":"https://pith.science/paper/TKAPLOVR"},"agent_actions":{"view_html":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS","download_json":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS.json","view_paper":"https://pith.science/paper/TKAPLOVR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04388&json=true","fetch_graph":"https://pith.science/api/pith-number/TKAPLOVRLORDYR77YYQZM543PS/graph.json","fetch_events":"https://pith.science/api/pith-number/TKAPLOVRLORDYR77YYQZM543PS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS/action/storage_attestation","attest_author":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS/action/author_attestation","sign_citation":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS/action/citation_signature","submit_replication":"https://pith.science/pith/TKAPLOVRLORDYR77YYQZM543PS/action/replication_record"}},"created_at":"2026-05-18T01:23:16.248368+00:00","updated_at":"2026-05-18T01:23:16.248368+00:00"}