{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KLFNIU2JYDV3CYUU3OQV476XEV","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":"5838b75156e39b06cc970167605e68f189cddb4eaae623bded6509f8dc45b232","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-05-24T12:22:53Z","title_canon_sha256":"5f0cb4915baf13a0031484e5505865384e6908ca703208229a3eeb87f7b236a8"},"schema_version":"1.0","source":{"id":"1705.08720","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08720","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08720v1","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08720","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"KLFNIU2JYDV3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KLFNIU2JYDV3CYUU","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KLFNIU2J","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:5006b6086dfc70f8f233ed2aff9106bc880c926121ff9328135cd6f10718bca1","target":"graph","created_at":"2026-05-18T00:43:44Z","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":"This work compares several node (and network) criticality measures quantifying to which extend each node is critical with respect to the communication flow between nodes of the network, and introduces a new measure based on the Bag-of-Paths (BoP) framework. Network disconnection simulation experiments show that the new BoP measure outperforms all the other measures on a sample of Erdos-Renyi and Albert-Barabasi graphs. Furthermore, a faster (still O(n^3)), approximate, BoP criticality relying on the Sherman-Morrison rank-one update of a matrix is introduced for tackling larger networks. This a","authors_text":"Bertrand Lebichot, Marco Saerens","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-05-24T12:22:53Z","title":"A Bag-of-Paths Node Criticality Measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08720","kind":"arxiv","version":1},"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":"sha256:6fe7a5b2e6c5ba5019eee30f4014454ff5162c8b93ae9f32d5704fe20d1d28ce","target":"record","created_at":"2026-05-18T00:43:44Z","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":"5838b75156e39b06cc970167605e68f189cddb4eaae623bded6509f8dc45b232","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-05-24T12:22:53Z","title_canon_sha256":"5f0cb4915baf13a0031484e5505865384e6908ca703208229a3eeb87f7b236a8"},"schema_version":"1.0","source":{"id":"1705.08720","kind":"arxiv","version":1}},"canonical_sha256":"52cad45349c0ebb16294dba15e7fd72546a45939a83c891891a08edf1c54d760","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52cad45349c0ebb16294dba15e7fd72546a45939a83c891891a08edf1c54d760","first_computed_at":"2026-05-18T00:43:44.445418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:44.445418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tGyCOjgsfBjEJNFYwJpKSXpTl4tPjaTHKH1cNZrP40pTYEqlAItpAzn+sVgnvoi99uS9PHNRD6GX62LACG8mBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:44.446080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08720","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe7a5b2e6c5ba5019eee30f4014454ff5162c8b93ae9f32d5704fe20d1d28ce","sha256:5006b6086dfc70f8f233ed2aff9106bc880c926121ff9328135cd6f10718bca1"],"state_sha256":"a95dc5f0e5ebc2a9ea6e8e62c8042bc81c12f545d510509f0aada6aec412cef5"}