{"paper":{"title":"Eigenvector dynamics under perturbation of modular networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IR"],"primary_cat":"physics.soc-ph","authors_text":"Peter A. Robinson, Sanjay Chawla, Santo Fortunato, Somwrita Sarkar","submitted_at":"2015-10-23T21:04:17Z","abstract_excerpt":"Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of $q$ communities, the number of eigenvectors corresponding to the $q$ largest eigenvalues form a \"community\" eigenspace and rotate together, but separately from that of the \"bulk\" eigenspace spanned by all the other eigenvectors. Using this property, the number of modules or clusters in a network can be estimated in an algorithm-independent way. A general argument and derivation for the theoretical detectability limit for sparse modular networks with $q$ communiti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07064","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"}