{"paper":{"title":"Clustering Spectrum of scale-free networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"A.J.E.M Janssen, Clara Stegehuis, Johan S.H. van Leeuwaarden, Remco van der Hofstad","submitted_at":"2017-06-06T12:21:32Z","abstract_excerpt":"Real-world networks often have power-law degrees and scale-free properties such as ultra-small distances and ultra-fast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the creation of triangles and signal the presence of hierarchy. We quantify this property in terms of $\\bar c(k)$, the probability that two neighbors of a degree-$k$ node are neighbors themselves. We investigate how the clustering spectrum $k\\mapsto\\bar c(k)$ scales with $k$ in the hidden variable model and show that $c(k)$ follows a {\\it universal curve} that con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01727","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"}