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In this paper we present a novel method on learning structural conjunction of image content by sparse graphical model. We first use matrix-variate distributions to formulate two statistical structure models and establish the connection between them. The connection leads us to sparse Gaussian graphical models in which sparse regression technique such as lasso is used for concentration matrix estimation as well as structure learning. Our proposed theoretical framework and structure selection methods provide an approach for exploiting structural conjunction of data. We apply this approach to construction of underlying structural correlation between image content, and demonstrate the effectiveness by solving image jigsaw problem.