{"paper":{"title":"Geometric Multiscale Community Detection: Markov Stability and Vector Partitioning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Mauricio Barahona, Zijing Liu","submitted_at":"2017-08-10T11:23:54Z","abstract_excerpt":"Multiscale community detection can be viewed from a dynamical perspective within the Markov Stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we reformulate multiscale community detection as a max-sum length vector partitioning problem with respect to the set of time-dependent node vectors expressed in terms of eigenvectors of the transition matrix. This formulation provides a geometric interpretation of Markov Stability in terms of a time-dependent spectral embedding, where the Markov time acts as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03167","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"}