{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:I5T7DBFYFMLHM2IG6R6EVIPG6S","short_pith_number":"pith:I5T7DBFY","schema_version":"1.0","canonical_sha256":"4767f184b82b16766906f47c4aa1e6f489b76687003fbd1eafd6b634ca7eb1c0","source":{"kind":"arxiv","id":"1808.06004","version":2},"attestation_state":"computed","paper":{"title":"Spectral Complexity of Directed Graphs and Application to Structural Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Igor Mezi\\'c, Maria Fonoberova, Tuhin Sahai, Vladimir A. Fonoberov","submitted_at":"2018-08-17T21:35:57Z","abstract_excerpt":"We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the spectrum of the recurrence matrix (associated with the reccurent part of the graph) and the Wasserstein distance. We show that the total complexity of the graph can then be defined in terms of the spectral complexity, complexities of individual components and edge weights. The essential property of the spectral complexity metric is that it accounts for directe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.06004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-08-17T21:35:57Z","cross_cats_sorted":[],"title_canon_sha256":"9f9a30e2652f21ab09e062ad97d5bd29750a011f15bb4c0ad71213565f8c4e19","abstract_canon_sha256":"166049ec7e12a85351b1d3a963bb7344eb6ad9d1a5df93e69def1426c0e01904"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.725520Z","signature_b64":"8HT5CGtPMlpsdA4AxPflNziAX7qy13beRpTvxdHkbdCOCPz5u0fFsptWAbG8TaMO8no50VdMdvFaNvTUbo5DDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4767f184b82b16766906f47c4aa1e6f489b76687003fbd1eafd6b634ca7eb1c0","last_reissued_at":"2026-05-18T00:01:48.724982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.724982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Complexity of Directed Graphs and Application to Structural Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Igor Mezi\\'c, Maria Fonoberova, Tuhin Sahai, Vladimir A. Fonoberov","submitted_at":"2018-08-17T21:35:57Z","abstract_excerpt":"We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the spectrum of the recurrence matrix (associated with the reccurent part of the graph) and the Wasserstein distance. We show that the total complexity of the graph can then be defined in terms of the spectral complexity, complexities of individual components and edge weights. The essential property of the spectral complexity metric is that it accounts for directe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06004","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.06004","created_at":"2026-05-18T00:01:48.725052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.06004v2","created_at":"2026-05-18T00:01:48.725052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06004","created_at":"2026-05-18T00:01:48.725052+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5T7DBFYFMLH","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5T7DBFYFMLHM2IG","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5T7DBFY","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S","json":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S.json","graph_json":"https://pith.science/api/pith-number/I5T7DBFYFMLHM2IG6R6EVIPG6S/graph.json","events_json":"https://pith.science/api/pith-number/I5T7DBFYFMLHM2IG6R6EVIPG6S/events.json","paper":"https://pith.science/paper/I5T7DBFY"},"agent_actions":{"view_html":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S","download_json":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S.json","view_paper":"https://pith.science/paper/I5T7DBFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.06004&json=true","fetch_graph":"https://pith.science/api/pith-number/I5T7DBFYFMLHM2IG6R6EVIPG6S/graph.json","fetch_events":"https://pith.science/api/pith-number/I5T7DBFYFMLHM2IG6R6EVIPG6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S/action/storage_attestation","attest_author":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S/action/author_attestation","sign_citation":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S/action/citation_signature","submit_replication":"https://pith.science/pith/I5T7DBFYFMLHM2IG6R6EVIPG6S/action/replication_record"}},"created_at":"2026-05-18T00:01:48.725052+00:00","updated_at":"2026-05-18T00:01:48.725052+00:00"}