{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:57IMNSDJAF4AEN5LC6CQWTVG6V","short_pith_number":"pith:57IMNSDJ","schema_version":"1.0","canonical_sha256":"efd0c6c86901780237ab17850b4ea6f552f87b610b75455d4a372c7d0786ad1e","source":{"kind":"arxiv","id":"1205.3630","version":3},"attestation_state":"computed","paper":{"title":"Alignment and integration of complex networks by hypergraph-based spectral clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","q-bio.MN","q-bio.QM"],"primary_cat":"physics.soc-ph","authors_text":"Bruno Nachtergaele, Tom Michoel","submitted_at":"2012-05-16T10:59:39Z","abstract_excerpt":"Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and computational methods to address these problems. Here we introduce a framework for clustering and community detection in such systems using hypergraph representations. Our main result is a generalization of the Perron-Frobenius theorem from which w"},"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":"1205.3630","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-05-16T10:59:39Z","cross_cats_sorted":["cs.SI","q-bio.MN","q-bio.QM"],"title_canon_sha256":"e828d0777fbdea301c7ddc09957b7e89082f394786584e7426383dcb6b2e684d","abstract_canon_sha256":"16fb28132a746ec75a406a388a50f9b78f905023d55bde4cdd430c7e425a64c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:51.646386Z","signature_b64":"OK6fRI4CBTfRNSyHWa5yjFBj+3OPYqmT0QrNtChdrhDx14I5Br4okvYmNMsclkzUAewswIgbaf3YnqnV7/DlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efd0c6c86901780237ab17850b4ea6f552f87b610b75455d4a372c7d0786ad1e","last_reissued_at":"2026-05-18T03:39:51.645788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:51.645788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alignment and integration of complex networks by hypergraph-based spectral clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","q-bio.MN","q-bio.QM"],"primary_cat":"physics.soc-ph","authors_text":"Bruno Nachtergaele, Tom Michoel","submitted_at":"2012-05-16T10:59:39Z","abstract_excerpt":"Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and computational methods to address these problems. Here we introduce a framework for clustering and community detection in such systems using hypergraph representations. Our main result is a generalization of the Perron-Frobenius theorem from which w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3630","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":"1205.3630","created_at":"2026-05-18T03:39:51.645877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.3630v3","created_at":"2026-05-18T03:39:51.645877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3630","created_at":"2026-05-18T03:39:51.645877+00:00"},{"alias_kind":"pith_short_12","alias_value":"57IMNSDJAF4A","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"57IMNSDJAF4AEN5L","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"57IMNSDJ","created_at":"2026-05-18T12:26:53.410803+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/57IMNSDJAF4AEN5LC6CQWTVG6V","json":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V.json","graph_json":"https://pith.science/api/pith-number/57IMNSDJAF4AEN5LC6CQWTVG6V/graph.json","events_json":"https://pith.science/api/pith-number/57IMNSDJAF4AEN5LC6CQWTVG6V/events.json","paper":"https://pith.science/paper/57IMNSDJ"},"agent_actions":{"view_html":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V","download_json":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V.json","view_paper":"https://pith.science/paper/57IMNSDJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.3630&json=true","fetch_graph":"https://pith.science/api/pith-number/57IMNSDJAF4AEN5LC6CQWTVG6V/graph.json","fetch_events":"https://pith.science/api/pith-number/57IMNSDJAF4AEN5LC6CQWTVG6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V/action/storage_attestation","attest_author":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V/action/author_attestation","sign_citation":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V/action/citation_signature","submit_replication":"https://pith.science/pith/57IMNSDJAF4AEN5LC6CQWTVG6V/action/replication_record"}},"created_at":"2026-05-18T03:39:51.645877+00:00","updated_at":"2026-05-18T03:39:51.645877+00:00"}