{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LTQQPZRGOC5V3IC6Z32QUXFJHP","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":"b827455f5003b63c95e1d7468a30fe5c2fed68b4a0e0b55a618a23cd20603ec4","cross_cats_sorted":["math.MG","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-08-11T09:06:47Z","title_canon_sha256":"69dfa186e732c051be698492024f20ebe3eb7bb9d12bdb83545f5eb4bb048ea0"},"schema_version":"1.0","source":{"id":"1608.03402","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03402","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03402v3","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03402","created_at":"2026-05-18T00:14:41Z"},{"alias_kind":"pith_short_12","alias_value":"LTQQPZRGOC5V","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LTQQPZRGOC5V3IC6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LTQQPZRG","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:81cda7b891f7471cea564c21b8108593b033c52f2c480e43ea6bf3a4b00583a6","target":"graph","created_at":"2026-05-18T00:14:41Z","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":"Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes of the subgraph lies entirely within the subgraph. According to our perception of convexity, convex network is such in which every connected subset of nodes induces a convex subgraph. We show that convexity is an inherent property of many networks that is not present in a random graph. Most convex are spatial infrastructure networks and social collaboration g","authors_text":"Lovro \\v{S}ubelj, Tilen Marc","cross_cats":["math.MG","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-08-11T09:06:47Z","title":"Convexity in complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03402","kind":"arxiv","version":3},"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:d0ea1a30cc6156d58a246ae7564c6fd0c48110e388f8d8e442f6c849bf661791","target":"record","created_at":"2026-05-18T00:14:41Z","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":"b827455f5003b63c95e1d7468a30fe5c2fed68b4a0e0b55a618a23cd20603ec4","cross_cats_sorted":["math.MG","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-08-11T09:06:47Z","title_canon_sha256":"69dfa186e732c051be698492024f20ebe3eb7bb9d12bdb83545f5eb4bb048ea0"},"schema_version":"1.0","source":{"id":"1608.03402","kind":"arxiv","version":3}},"canonical_sha256":"5ce107e62670bb5da05ecef50a5ca93bf86d82996c955a363f45ec5b48c80987","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ce107e62670bb5da05ecef50a5ca93bf86d82996c955a363f45ec5b48c80987","first_computed_at":"2026-05-18T00:14:41.452107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:41.452107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PI0oe+KCjg7wxO+4MtmmIR/XL8LyUr3BLth4CMEaJYuljuKrMDEkDMnp3jRY65/BPFh0UQc8YzDryupJEQamCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:41.452735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03402","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0ea1a30cc6156d58a246ae7564c6fd0c48110e388f8d8e442f6c849bf661791","sha256:81cda7b891f7471cea564c21b8108593b033c52f2c480e43ea6bf3a4b00583a6"],"state_sha256":"1aae69717cf8c31666e6106c9f4c545fe149beb44f034d94d70f424d924ad5bc"}