{"paper":{"title":"Random Graphs Associated to some Discrete and Continuous Time Preferential Attachment Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Angelica Pachon, Federico Polito, Laura Sacerdote","submitted_at":"2015-03-20T16:40:42Z","abstract_excerpt":"We give a common description of Simon, Barab\\'asi--Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barab\\'asi--Albert model coincides with the asymptotic in-degree distribution of the Simon model. Furthermore, we show that when the number of vertices in the Simon model (with parameter $\\alpha$) goes to infinity, a portion of them behave as a Yule model with parameters $(\\lambda,\\beta) = (1-\\alpha,1)$, and through thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06150","kind":"arxiv","version":4},"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"}