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We propose a novel sparse matrix graphical model for matrix-variate data.By penalizing the row and column precision matrices, our method gives sparse estimates of these matrices.The resulting estimates present row and column conditional iudependence graphical models and are more parsimonious than the usual sparse vector-variate graphical models.Asymptotic analysis shows that the resulting estimates enjoy better rate of convergence than the vector-variate graphical model.The finite sample performance of the proposed method is illustrated via simulation studies and analysis of real data.