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As an effective modeling tool, normal distribution Gaussian mixture model is of great theoretical significance. In this paper, we detect the community structure of Zachary network with Gaussian mixture model. We use singular value decomposition (SVD) to transform the network to vector, which maintains the similarities among nodes, and then apply Gaussian mixture model to detect the community structure. Experiments show that it has very high accuracy. We also build up a framework that may incorporate other clustering methods.