{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:X5BXC3AIJ6V5XCBZNSSBWD7PIX","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":"abb8f85bf1a2abd1506f0ba2503b53e93f6f6c2761fe2bef46d17f4d51d8f46a","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-06-05T15:54:50Z","title_canon_sha256":"2d7aca188d173b6083108ee8aa043e0a33e60ddb6fa8a65d2b43ff58dbb2b9d6"},"schema_version":"1.0","source":{"id":"1806.01757","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01757","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01757v2","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01757","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"X5BXC3AIJ6V5","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X5BXC3AIJ6V5XCBZ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X5BXC3AI","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:8eb38bff6e3fae996ad3f9eabd48523c9d251b84e543d95a7b3614c4fbe5b995","target":"graph","created_at":"2026-05-18T00:13:43Z","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":"In a network, the shortest paths between nodes are of great importance as they allow the fastest and strongest interaction between nodes. However measuring the shortest paths between all nodes in a large network is computationally expensive. In this paper we propose a method to estimate the shortest path length (SPL) distribution of a network by random walk sampling. To deal with the unequal inclusion probabilities of dyads (pairs of nodes) in the sample, we generalize the usage of Hansen-Hurwitz estimator and Horvitz-Thompson estimator (and their ratio forms) and apply them to the sampled dya","authors_text":"Bruce D. Spencer, Minhui Zheng","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-06-05T15:54:50Z","title":"Estimating Shortest Path Length Distributions via Random Walk Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01757","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:a4f5a572db3eac3e252d2adf588cd774bc49cf1671dfe8628d8ac20be24f1ee6","target":"record","created_at":"2026-05-18T00:13:43Z","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":"abb8f85bf1a2abd1506f0ba2503b53e93f6f6c2761fe2bef46d17f4d51d8f46a","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-06-05T15:54:50Z","title_canon_sha256":"2d7aca188d173b6083108ee8aa043e0a33e60ddb6fa8a65d2b43ff58dbb2b9d6"},"schema_version":"1.0","source":{"id":"1806.01757","kind":"arxiv","version":2}},"canonical_sha256":"bf43716c084fabdb88396ca41b0fef45e8b96f6aeded6774279359ce83c4f12b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf43716c084fabdb88396ca41b0fef45e8b96f6aeded6774279359ce83c4f12b","first_computed_at":"2026-05-18T00:13:43.976163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:43.976163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RmS0nBJqNZ3qPKkkjGgNEDiz+6CyZeuFAC2/xC1O5Avq6Vsgrh0VZiQrr+6GmABWn7dTErR/GqUGJn8/KlyGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:43.976860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01757","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f5a572db3eac3e252d2adf588cd774bc49cf1671dfe8628d8ac20be24f1ee6","sha256:8eb38bff6e3fae996ad3f9eabd48523c9d251b84e543d95a7b3614c4fbe5b995"],"state_sha256":"21201db0361a824a4e2ba146e2874f45e5893396ffa1a68e3fff7be10b83c030"}