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Identifying clusters of arbitrary shapes remains a challenge in the field of data clustering. We propose a new measure of cluster quality based on minimizing the penalty of disconnection between objects that would be ideally clustered together. This disconnectivity is based on analysis of nearest neighbors and the principle that an object should be in the same cluster as its nearest neighbors. An algorithm called MinDisconnect is proposed that heuristically minimizes disconnectivity and numerical results are presented that indicate that the new algorithm can effectively identify clusters of complex shapes and is robust in finding clusters of arbitrary shapes.