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Community is tightly-connected group of agents in social networks and the discovery of such subgraphs has aroused considerable research interest in the past few years. Typically, a quantity function called modularity is used to guide the division of the network. By representing the network as a bipartite graph between its vertices and cliques, we show that community structure can be uncovered by the correlation coefficients derived from the bipartite graph through a suitable optimization procedure. We also show that the modularity can be seen as a special case of the quantity function built from the covariance of the vertices. Due the the heteroscedaticity, the modularity suffers a resolution limit problem. And the quantity function based on correlation proposed here exhibits higher resolution power. Experiments show that the proposed method can achieve promising results on synthesized and real world networks. It outperforms several state-of-the-art algorithms.