{"paper":{"title":"Renormalisation of Inhomogeneous Random Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Diego Garlaschelli, Frank den Hollander, Luca Avena, Rajat Subhra Hazra","submitted_at":"2026-07-14T07:41:58Z","abstract_excerpt":"We consider inhomogeneous random graphs in which vertices are assigned i.i.d.\\ random weights, pairs of distinct vertices are connected by an edge independently with a probability that is a bi-variate function of the weights of the vertices, and single vertices are connected to themselves by a self-loop independently with a probability that is a uni-variate function of the weight of the vertex. We apply a renormalisation transformation in which vertices are aggregated into groups of equal size according to a greedy algorithm, namely, distinct groups of aggregated vertices are connected by an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12459","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12459/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}