{"paper":{"title":"On the dense Preferential Attachment Graph models and their graphon induced counterpart","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"\\'Agnes Backhausz, D\\'avid Kunszenti-Kov\\'acs","submitted_at":"2017-01-24T08:04:29Z","abstract_excerpt":"Letting $\\mathcal{M}$ denote the space of finite measures on $\\mathbb{N}$, and $\\mu_\\lambda\\in\\mathcal{M}$ denote the Poisson distribution with parameter $\\lambda$, the function $W:[0,1]^2\\to\\mathcal{M}$ given by \\[ W(x,y)=\\mu_{c\\log x\\log y} \\] is called the PAG graphon with density $c$. It is known that this is the limit, in the multigraph homomorphism sense, of the dense Preferential Attachment Graph (PAG) model with edge density $c$. This graphon can then in turn be used to generate the so-called W-random graphs in a natural way. The aim of this paper is to compare the dense PAG model with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06760","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"}