{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UXQIC2II5UWLUAIRQDD3Z47P5V","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":"4fdff23cfa70471fc38358c7bab546e10b8bba2296f08d4ed00f7999b1208c9e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-18T14:29:41Z","title_canon_sha256":"81136e51d1cce19fb22970483983e747bd104df57e253072380c8a3ceb1673e9"},"schema_version":"1.0","source":{"id":"1505.04658","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04658","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04658v2","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04658","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"UXQIC2II5UWL","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UXQIC2II5UWLUAIR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UXQIC2II","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:836d3a6a717cb023a6c1e85ca970b4820b6d7cc4e65f8d69d801d8aeb0709e64","target":"graph","created_at":"2026-05-18T02:05:23Z","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":"The entropy of a graph was first introduced by Rashevsky \\cite{Rashevsky} and Trucco \\cite{Trucco} to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of definitions of graph entropy measures and generalized graph entropies. Then we survey the known results about them from the following three respects: inequalities and extremal properties on graph entropies, relationships between graph structures, graph energies, topological indices and generalized graph entropies, complexity for calculation of graph entropie","authors_text":"Meiqin Wei, Xueliang Li","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-18T14:29:41Z","title":"A survey of recent results in (generalized) graph entropies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04658","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:b57453c0e5878806b65dc1f8ddcd1d59edd7a344bd753b3cdb5af4b63cc2f84c","target":"record","created_at":"2026-05-18T02:05:23Z","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":"4fdff23cfa70471fc38358c7bab546e10b8bba2296f08d4ed00f7999b1208c9e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-18T14:29:41Z","title_canon_sha256":"81136e51d1cce19fb22970483983e747bd104df57e253072380c8a3ceb1673e9"},"schema_version":"1.0","source":{"id":"1505.04658","kind":"arxiv","version":2}},"canonical_sha256":"a5e0816908ed2cba011180c7bcf3efed6f92f1b28161ecfea83ddc6c6249f331","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5e0816908ed2cba011180c7bcf3efed6f92f1b28161ecfea83ddc6c6249f331","first_computed_at":"2026-05-18T02:05:23.246784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:23.246784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WxLuPHT+RsvJiq+phv4rhbH5U/fx6BdpqSZ7a6JroDsv4OWkOcI5drFRMFQS4n117bDmmeutyV994jd88dgWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:23.247531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04658","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b57453c0e5878806b65dc1f8ddcd1d59edd7a344bd753b3cdb5af4b63cc2f84c","sha256:836d3a6a717cb023a6c1e85ca970b4820b6d7cc4e65f8d69d801d8aeb0709e64"],"state_sha256":"f033c70d824532dcd5a10b0761e76190810e55723139f49866f748e4d88c146f"}