2026-09-19T15:33:56Zhttps://digital.lib.washington.edu/server/oai/request

oai:digital.lib.washington.edu:1773/406362026-02-15T22:34:45Zcom_1773_4888col_1773_4939

Dumitriu, Ioana Hoffman, Christopher Brito, Gerandy 2017-10-26T20:51:45Z 2017-10-26T20:51:45Z 2017-10-26 2017-08 Brito_washington_0250E_17725.pdf http://hdl.handle.net/1773/40636 Thesis (Ph.D.)--University of Washington, 2017-08 This thesis concerns to spectral gap of random regular graphs and consists of two main con- tributions. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for the non trivial eigenvalues of its adjacency operator, proving Alon's Conjecture for this family of graphs. Secondly, we use a spectral algorithm to recover hidden communities in a random network model we call regular stochastic block model. We rely on a technique introduced recently by Massoullie, which we develop here for random regular graphs. application/pdf en_US CC BY-NC community detection regular graphs spectral analysis spectral gap Mathematics Mathematics Spectral analysis in bipartite biregular graphs and community detection Thesis Open Access open.access