{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IZ33FJBDGQDE667TGIDOFNBEOX","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":"4746bc4f67711b5c8914ab751fd83b9b0f4547c3a53ffe1fbeac7595fde75cdf","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-04-12T22:03:26Z","title_canon_sha256":"03065128e6ec9ecf7365dc91da2e8c57bd361b884042a3c0ca3aacbc1dc49ce2"},"schema_version":"1.0","source":{"id":"1704.03943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03943","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03943v1","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03943","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"pith_short_12","alias_value":"IZ33FJBDGQDE","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IZ33FJBDGQDE667T","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IZ33FJBD","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:12db660442aa7521f002009a85d73ea80439bd3542aced9eb5751df0be00c8ab","target":"graph","created_at":"2026-05-18T00:46:25Z","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":"Degree ssortativity is the tendency for nodes of high degree (resp.low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is sually quantified by the Pearson correlation coefficient of the degree-degree correlation. Here we extend this concept to account for the effect of second neighbours to a given node in a graph. That is, we consider the two-walks degree of a node as the sum of all the degrees of its adjacent nodes. The two-walks degree assortativity of a graph is then the Pearson correlation coefficient of the two-walks degree-degree correlation. We fou","authors_text":"Alfonso Allen-Perkins, Ernesto Estrada, Juan Manuel Pastor","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-04-12T22:03:26Z","title":"Two-walks degree assortativity in graphs and networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03943","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":"sha256:54305f73bf5034c94440bef6c419d0d5d1b40f9b8f1b89ad9aa248eeedf093c3","target":"record","created_at":"2026-05-18T00:46:25Z","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":"4746bc4f67711b5c8914ab751fd83b9b0f4547c3a53ffe1fbeac7595fde75cdf","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2017-04-12T22:03:26Z","title_canon_sha256":"03065128e6ec9ecf7365dc91da2e8c57bd361b884042a3c0ca3aacbc1dc49ce2"},"schema_version":"1.0","source":{"id":"1704.03943","kind":"arxiv","version":1}},"canonical_sha256":"4677b2a42334064f7bf33206e2b42475fc82d445e74191c8a3b6cbe6b310e39b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4677b2a42334064f7bf33206e2b42475fc82d445e74191c8a3b6cbe6b310e39b","first_computed_at":"2026-05-18T00:46:25.821978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:25.821978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vQOPx9BtAHDki0OIJwPsPhFDpndoqHmQXo1lKQT4GYLmAVpyEk+TjZYT04Q0jC83QPEAkMgalvyA7enUjvsJBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:25.822584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54305f73bf5034c94440bef6c419d0d5d1b40f9b8f1b89ad9aa248eeedf093c3","sha256:12db660442aa7521f002009a85d73ea80439bd3542aced9eb5751df0be00c8ab"],"state_sha256":"f3ac71bb6b383f22e059ad8567e1a6addcb132f4c5df41f6605f6de071a522be"}