In this paper, we study community detection when we observe $m$ sparsenetworks and a high dimensional covariate matrix, all encoding the same community structure among $n$ subjects . In the asymptotic regime where thenumber of features and the number of subjects $p$ grows proportionally, we find a sharp threshold of phase transition . The formula implies the necessity of integrating information from multiple datasources. Consequently, it induces a sharp . threshold of . detection (i.e., weak recovery) is possible in regime where detection is possible and the . regimewhere no procedure performs better than a random guess. No procedure performs best than a . random guess, we say. In the special case

Author(s) : Zongming Ma, Sagnik Nandy

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Keywords : detection - community - threshold - sharp - guess -

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