{"paper":{"title":"Islands of stability in motif distributions of random networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A.B. Shkarin, M.V. Tamm, O.V. Valba, S.K. Nechaev, V.A. Avetisov","submitted_at":"2013-06-29T15:17:01Z","abstract_excerpt":"We consider random non-directed networks subject to dynamics conserving vertex degrees and study analytically and numerically equilibrium three-vertex motif distributions in the presence of an external field, $h$, coupled to one of the motifs. For small $h$ the numerics is well described by the \"chemical kinetics\" for the concentrations of motifs based on the law of mass action. For larger $h$ a transition into some trapped motif state occurs in Erd\\H{o}s-R\\'enyi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0113","kind":"arxiv","version":2},"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"}