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We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyse the effect of inter-community ‘noise’ (inter-community edges) on any ‘community detection’ algorithm&#39;s ability to correctly group nodes assigned to a planted partition, a problem which has been proved to be NP complete in a standard rendition. O...

Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs