{"paper":{"title":"Fluctuations of motifs and non self-averaging in complex networks. A self- vs non-self-averaging phase transition scenario","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.data-an"],"primary_cat":"cond-mat.dis-nn","authors_text":"Massimo Ostilli","submitted_at":"2013-06-24T10:30:58Z","abstract_excerpt":"Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been observed when the exponent $\\gamma$ of the associated power law degree-distribution is sufficiently small. In particular, a zero percolation threshold takes place for $\\gamma<3$, and an anomalous critical behavior sets in for $\\gamma<5$. In this Letter we prove that in sparse scale-free networks characterized by a cut-off scaling with the sistem size $N$, relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5565","kind":"arxiv","version":3},"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"}