{"paper":{"title":"Maximizing the size of the giant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pieter Trapman, Tom Britton","submitted_at":"2010-10-04T10:06:22Z","abstract_excerpt":"We consider two classes of random graphs: $(a)$ Poissonian random graphs in which the $n$ vertices in the graph have i.i.d.\\ weights distributed as $X$, where $\\mathbb{E}(X) = \\mu$. Edges are added according to a product measure and the probability that a vertex of weight $x$ shares and edge with a vertex of weight $y$ is given by $1-e^{-xy/(\\mu n)}$. $(b)$ A thinned configuration model in which we create a ground-graph in which the $n$ vertices have i.i.d.\\ ground-degrees, distributed as $D$, with $\\mathbb{E}(D) = \\mu$. The graph of interest is obtained by deleting edges independently with pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0524","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"}