{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EB7BONDHJXWOYKX2ME7RPVSNSA","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":"d7c9b1781372539c8cf99483aaa5314055f63626d70537886f63e5e5a71c56c8","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-07T18:30:40Z","title_canon_sha256":"0f6300c569df7fcbfdf81eb7a7971795e553d19bd8c09d0109cd57eaad5135e1"},"schema_version":"1.0","source":{"id":"1802.02556","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02556","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02556v2","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02556","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"EB7BONDHJXWO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EB7BONDHJXWOYKX2","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EB7BONDH","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:c05f8c51d2bd57f865dc0e52ff8fa446c623709be136e0406aaa57b81c5dbc90","target":"graph","created_at":"2026-05-17T23:53:01Z","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":"Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the problem of finding a subset $S$ of $k$ vertices to maximize its CFCC $C(S)$, both theoretically and experimentally. We show that the problem is NP-hard, but propose two greedy algorithms for minimizing the reciprocal of $C(S)$ with provable guarantees using the monotoncity and supermodularity. The first is a deterministic algorithm with an approximation fac","authors_text":"Huan Li, Liren Shan, Richard Peng, Yuhao Yi, Zhongzhi Zhang","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-07T18:30:40Z","title":"Current Flow Group Closeness Centrality for Complex Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02556","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":"sha256:0eb45870a4a0ebf6254cf03ef5d67110d032939786c595f4769bffa8c6bac41d","target":"record","created_at":"2026-05-17T23:53:01Z","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":"d7c9b1781372539c8cf99483aaa5314055f63626d70537886f63e5e5a71c56c8","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-07T18:30:40Z","title_canon_sha256":"0f6300c569df7fcbfdf81eb7a7971795e553d19bd8c09d0109cd57eaad5135e1"},"schema_version":"1.0","source":{"id":"1802.02556","kind":"arxiv","version":2}},"canonical_sha256":"207e1734674decec2afa613f17d64d900b4467a388ab0b0d4fe747512590ea4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"207e1734674decec2afa613f17d64d900b4467a388ab0b0d4fe747512590ea4b","first_computed_at":"2026-05-17T23:53:01.288068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:01.288068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KzaQBSN7Mbbe8WNyz44xKeL4ZRmFhhSppSBqAy+AKuwyQkOAtP/ZVydOXU2UAB2ioBCXWqo4QtoQldWHeX79Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:01.288639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02556","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eb45870a4a0ebf6254cf03ef5d67110d032939786c595f4769bffa8c6bac41d","sha256:c05f8c51d2bd57f865dc0e52ff8fa446c623709be136e0406aaa57b81c5dbc90"],"state_sha256":"ef62fc038f8e9bd1f4bef4207a00554e958d91b48d809dd10e73453f40e8df83"}