{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3YBELRLY4KII2IRBVJ2P3YHL2N","short_pith_number":"pith:3YBELRLY","schema_version":"1.0","canonical_sha256":"de0245c578e2908d2221aa74fde0ebd36ee19c3122fe57e9eab8a84b0a0f38c4","source":{"kind":"arxiv","id":"1509.07715","version":1},"attestation_state":"computed","paper":{"title":"Uncovering the Small Community Structure in Large Networks: A Local Spectral Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"David Bindel, John Hopcroft, Kun He, Yixuan Li","submitted_at":"2015-09-25T13:50:34Z","abstract_excerpt":"Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify"},"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":"1509.07715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-09-25T13:50:34Z","cross_cats_sorted":["cs.DS","physics.soc-ph"],"title_canon_sha256":"94a439cde916357fb03dca806d789caa1d69b35987377804415bee8590c7cd23","abstract_canon_sha256":"e2441bce1efe40c4ef97ba9e1342c94620c578e11e1f59df1f0c1b006acc1adf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:02.098788Z","signature_b64":"a+MBHO9OrOMLxZeuUwiGouL1X7gaOLpjmUppViixbY3hA+3DtK9oH95gxABwBiw0mXm+bl1GPNjKkOj2nkAjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de0245c578e2908d2221aa74fde0ebd36ee19c3122fe57e9eab8a84b0a0f38c4","last_reissued_at":"2026-05-18T01:32:02.098394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:02.098394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uncovering the Small Community Structure in Large Networks: A Local Spectral Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"David Bindel, John Hopcroft, Kun He, Yixuan Li","submitted_at":"2015-09-25T13:50:34Z","abstract_excerpt":"Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07715","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":"1509.07715","created_at":"2026-05-18T01:32:02.098456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07715v1","created_at":"2026-05-18T01:32:02.098456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07715","created_at":"2026-05-18T01:32:02.098456+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YBELRLY4KII","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YBELRLY4KII2IRB","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YBELRLY","created_at":"2026-05-18T12:29:02.477457+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/3YBELRLY4KII2IRBVJ2P3YHL2N","json":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N.json","graph_json":"https://pith.science/api/pith-number/3YBELRLY4KII2IRBVJ2P3YHL2N/graph.json","events_json":"https://pith.science/api/pith-number/3YBELRLY4KII2IRBVJ2P3YHL2N/events.json","paper":"https://pith.science/paper/3YBELRLY"},"agent_actions":{"view_html":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N","download_json":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N.json","view_paper":"https://pith.science/paper/3YBELRLY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07715&json=true","fetch_graph":"https://pith.science/api/pith-number/3YBELRLY4KII2IRBVJ2P3YHL2N/graph.json","fetch_events":"https://pith.science/api/pith-number/3YBELRLY4KII2IRBVJ2P3YHL2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N/action/storage_attestation","attest_author":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N/action/author_attestation","sign_citation":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N/action/citation_signature","submit_replication":"https://pith.science/pith/3YBELRLY4KII2IRBVJ2P3YHL2N/action/replication_record"}},"created_at":"2026-05-18T01:32:02.098456+00:00","updated_at":"2026-05-18T01:32:02.098456+00:00"}