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The problem of finding clusters in a graph arises in several applications such as social networks, data mining and computer networks. A typical, convex optimization-approach, that is often adopted is to identify a sparse plus low-rank decomposition of the adjacency matrix of the graph, with the (dense) low-rank component representing the clusters. In this paper, we sharply characterize the conditions for successfully identifying clusters using this approach. In particular, we introduce thedoi:10.1109/icassp.2014.6855219 dblp:conf/icassp/VinayakOH14 fatcat:3z7rkihtejchbgdfjictvugtpe