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Many real-world networks exhibit a community structure: The vertices of the network are partitioned into groups such that the concentration of linkages is high among vertices in the same group and low otherwise. This motivates us to introduce a class of Gaussian graphical models with a community structure that replicates this empirical regularity. A natural question that arises in this framework is how to detect the communities from a random sample of observations. We introduce an algorithmdoi:10.2139/ssrn.2776505 fatcat:te4wyvhswjb43malowkqbmae3y