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One of the most useful measures of cluster quality is the modularity of the partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random graph. In this paper, we show that the problem of finding a partition maximizing the modularity of a given graph $(G)$ can be reduced to a minimum weighted cut (MWC) problem on a complete graph with the same vertices as $(G)$. We then show that the resulting minimum cut problem can be efficiently solved by adapting existing graph partitioning techniques. Our algorithm finds clusterings of a comparable quality and is much faster than the existing clustering algorithms.