{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:PKOQOQGXJUA5T4UG3LKPTGDLBG","short_pith_number":"pith:PKOQOQGX","schema_version":"1.0","canonical_sha256":"7a9d0740d74d01d9f286dad4f9986b09b687f05b2b286db8132b339fb20922a2","source":{"kind":"arxiv","id":"0908.3436","version":1},"attestation_state":"computed","paper":{"title":"Rank-based attachment leads to power law graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Jeannette Janssen, Pawel Pralat","submitted_at":"2009-08-24T15:21:52Z","abstract_excerpt":"We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power -a, for some a in (0,1). Through a rigorous analysis, we show that rank-based attachment models lead to graphs with a power law degree distribution with exponent 1+1/a whenever vertices are ranked according to their degree, their age, or a randomly chosen fitness value. We also investigate the case where the ranking is b"},"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":"0908.3436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-24T15:21:52Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e1af332b927fff87dfa6e15a3a01130d737b7c9fce17b269116b40faceadb227","abstract_canon_sha256":"233375c14ae37c26870b616f57f413f9a4c3a2e49bde9d57dad264d35216734b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:09.086299Z","signature_b64":"aH68PPKSPNQ3Y4qPYLMSQcmA8GQymKsiiwEDgH2tIBPyqK2HmiJrd8xdRfYJaHmI+1ht+oRBviAf8Be4mDepBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a9d0740d74d01d9f286dad4f9986b09b687f05b2b286db8132b339fb20922a2","last_reissued_at":"2026-05-18T03:47:09.085786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:09.085786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank-based attachment leads to power law graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Jeannette Janssen, Pawel Pralat","submitted_at":"2009-08-24T15:21:52Z","abstract_excerpt":"We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power -a, for some a in (0,1). Through a rigorous analysis, we show that rank-based attachment models lead to graphs with a power law degree distribution with exponent 1+1/a whenever vertices are ranked according to their degree, their age, or a randomly chosen fitness value. We also investigate the case where the ranking is b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3436","kind":"arxiv","version":1},"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":"0908.3436","created_at":"2026-05-18T03:47:09.085867+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.3436v1","created_at":"2026-05-18T03:47:09.085867+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3436","created_at":"2026-05-18T03:47:09.085867+00:00"},{"alias_kind":"pith_short_12","alias_value":"PKOQOQGXJUA5","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PKOQOQGXJUA5T4UG","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PKOQOQGX","created_at":"2026-05-18T12:26:01.383474+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/PKOQOQGXJUA5T4UG3LKPTGDLBG","json":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG.json","graph_json":"https://pith.science/api/pith-number/PKOQOQGXJUA5T4UG3LKPTGDLBG/graph.json","events_json":"https://pith.science/api/pith-number/PKOQOQGXJUA5T4UG3LKPTGDLBG/events.json","paper":"https://pith.science/paper/PKOQOQGX"},"agent_actions":{"view_html":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG","download_json":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG.json","view_paper":"https://pith.science/paper/PKOQOQGX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.3436&json=true","fetch_graph":"https://pith.science/api/pith-number/PKOQOQGXJUA5T4UG3LKPTGDLBG/graph.json","fetch_events":"https://pith.science/api/pith-number/PKOQOQGXJUA5T4UG3LKPTGDLBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG/action/storage_attestation","attest_author":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG/action/author_attestation","sign_citation":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG/action/citation_signature","submit_replication":"https://pith.science/pith/PKOQOQGXJUA5T4UG3LKPTGDLBG/action/replication_record"}},"created_at":"2026-05-18T03:47:09.085867+00:00","updated_at":"2026-05-18T03:47:09.085867+00:00"}