{"paper":{"title":"Finite-size effects in exponential random graphs and cluster evaporation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-th"],"primary_cat":"cond-mat.dis-nn","authors_text":"A. Gorsky, O. Valba","submitted_at":"2019-05-08T21:01:51Z","abstract_excerpt":"In this Letter we find numerically the strong finite-size effects in the critical behavior of Erd\\H{o}s-R\\'enyi (ER) networks supplemented with chemical potentials for some motifs, in particular 2-stars and triangles. For the 2-star model above the critical value of the chemical potential a ground state looks as star-like graph with the finite set of hubs at ER parameter $p<0.5$ or as the single cluster at $p>0.5$. It is found that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover and at $N>N^{*}(p)$ the network flows via a cluste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03336","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"}