{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:S7RGTFGEOZI2LJ4XSFOJGGYUVS","short_pith_number":"pith:S7RGTFGE","canonical_record":{"source":{"id":"1101.1703","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-10T03:31:15Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"afad6e1a441fa47e16aff66ce33214cb51095a84508c1bfe7e4083e407c6cc44","abstract_canon_sha256":"083a2af3b680acf16469dd30297e21d66f7587062f127e629f94e7118f09e74a"},"schema_version":"1.0"},"canonical_sha256":"97e26994c47651a5a797915c931b14ac92219825d78e8eff60910700b9902eac","source":{"kind":"arxiv","id":"1101.1703","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1703","created_at":"2026-05-18T02:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1703v2","created_at":"2026-05-18T02:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1703","created_at":"2026-05-18T02:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"S7RGTFGEOZI2","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S7RGTFGEOZI2LJ4X","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S7RGTFGE","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:S7RGTFGEOZI2LJ4XSFOJGGYUVS","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1703","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-10T03:31:15Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"afad6e1a441fa47e16aff66ce33214cb51095a84508c1bfe7e4083e407c6cc44","abstract_canon_sha256":"083a2af3b680acf16469dd30297e21d66f7587062f127e629f94e7118f09e74a"},"schema_version":"1.0"},"canonical_sha256":"97e26994c47651a5a797915c931b14ac92219825d78e8eff60910700b9902eac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:43.765553Z","signature_b64":"WUx1FZONjuMGQhcxUkeNWsv496A62twbqRQQdjaSBB/j74atYVIv4PjdmC0N+QVYqTyWyWku/4byXHJbA6xTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97e26994c47651a5a797915c931b14ac92219825d78e8eff60910700b9902eac","last_reissued_at":"2026-05-18T02:03:43.764967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:43.764967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1703","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/zIZifeR3ppZxVWS/Fdrokbzyj73eIuCBW7rJuWyWuRpcKc1tb/ezRXMYpddYCq3oezme5LU8upZ1ZOoNpASCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:29:14.996233Z"},"content_sha256":"9e830dab41170d00cd5d6617643af2b00dc73120e4d2f3d2676e49383c2fda04","schema_version":"1.0","event_id":"sha256:9e830dab41170d00cd5d6617643af2b00dc73120e4d2f3d2676e49383c2fda04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:S7RGTFGEOZI2LJ4XSFOJGGYUVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Detecting Important Nodes to Community Structure Using the Spectrum of the Graph","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Yang Wang, Ying Fan, Zengru Di","submitted_at":"2011-01-10T03:31:15Z","abstract_excerpt":"Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem. In this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1703","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/Pd4huuBi+prAOBk6gFMiBlzYxGkRKdqX4Qp6uKlC0tkR1Rst8IhE4zj1x04KtuaxNFblxlAvQhN4lpZLd0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:29:14.996598Z"},"content_sha256":"770795e576e59006861e1e752de888c9fbebccaee00732848bc6394edce94fcf","schema_version":"1.0","event_id":"sha256:770795e576e59006861e1e752de888c9fbebccaee00732848bc6394edce94fcf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7RGTFGEOZI2LJ4XSFOJGGYUVS/bundle.json","state_url":"https://pith.science/pith/S7RGTFGEOZI2LJ4XSFOJGGYUVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7RGTFGEOZI2LJ4XSFOJGGYUVS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T00:29:14Z","links":{"resolver":"https://pith.science/pith/S7RGTFGEOZI2LJ4XSFOJGGYUVS","bundle":"https://pith.science/pith/S7RGTFGEOZI2LJ4XSFOJGGYUVS/bundle.json","state":"https://pith.science/pith/S7RGTFGEOZI2LJ4XSFOJGGYUVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7RGTFGEOZI2LJ4XSFOJGGYUVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:S7RGTFGEOZI2LJ4XSFOJGGYUVS","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":"083a2af3b680acf16469dd30297e21d66f7587062f127e629f94e7118f09e74a","cross_cats_sorted":["cs.SI"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-10T03:31:15Z","title_canon_sha256":"afad6e1a441fa47e16aff66ce33214cb51095a84508c1bfe7e4083e407c6cc44"},"schema_version":"1.0","source":{"id":"1101.1703","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1703","created_at":"2026-05-18T02:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1703v2","created_at":"2026-05-18T02:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1703","created_at":"2026-05-18T02:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"S7RGTFGEOZI2","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S7RGTFGEOZI2LJ4X","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S7RGTFGE","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:770795e576e59006861e1e752de888c9fbebccaee00732848bc6394edce94fcf","target":"graph","created_at":"2026-05-18T02:03:43Z","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":"Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem. In this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change ","authors_text":"Yang Wang, Ying Fan, Zengru Di","cross_cats":["cs.SI"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-10T03:31:15Z","title":"Detecting Important Nodes to Community Structure Using the Spectrum of the Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1703","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":"sha256:9e830dab41170d00cd5d6617643af2b00dc73120e4d2f3d2676e49383c2fda04","target":"record","created_at":"2026-05-18T02:03:43Z","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":"083a2af3b680acf16469dd30297e21d66f7587062f127e629f94e7118f09e74a","cross_cats_sorted":["cs.SI"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-10T03:31:15Z","title_canon_sha256":"afad6e1a441fa47e16aff66ce33214cb51095a84508c1bfe7e4083e407c6cc44"},"schema_version":"1.0","source":{"id":"1101.1703","kind":"arxiv","version":2}},"canonical_sha256":"97e26994c47651a5a797915c931b14ac92219825d78e8eff60910700b9902eac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e26994c47651a5a797915c931b14ac92219825d78e8eff60910700b9902eac","first_computed_at":"2026-05-18T02:03:43.764967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:43.764967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WUx1FZONjuMGQhcxUkeNWsv496A62twbqRQQdjaSBB/j74atYVIv4PjdmC0N+QVYqTyWyWku/4byXHJbA6xTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:43.765553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1703","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e830dab41170d00cd5d6617643af2b00dc73120e4d2f3d2676e49383c2fda04","sha256:770795e576e59006861e1e752de888c9fbebccaee00732848bc6394edce94fcf"],"state_sha256":"0b4e00b087713065de958d8b2465f461686a0da0b488c62b2fd812c63488d06a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6K/027qL3/MVj1q6Ns0FZf88khKVKpQcELNB48fZta1pEkoLZ7K3Gj5TjWIvE1Sh1Rrybm2axiPUIojIrwgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:29:14.998507Z","bundle_sha256":"bba95a564cf2502cfbd90dd0dd590573822ed1af1546f31cdc186aa9e14e9f43"}}