Modeling noisy data in a network context remains an unavoidable obstacle; fortunately, random matrix theory may comprehensively describe network environments. Noisy data necessitates the probabilistic characterization of these networks using matrix variate models. Denoising network data using a Bayesian approach is not common in surveyed literature. Therefore, this paper adopts the Bayesian viewpoint and introduces a new version of the matrix variate t graphical network. This model\\\\\\\'s prior beliefs rely on the matrix variate gamma distribution to handle the noise process flexibly; from a statistical learning viewpoint, such a theoretical consideration benefits the comprehension of structures and processes that cause network-based noise in data as part of machine learning and offers real-world interpretation. A proposed Gibbs algorithm is provided for computing and approximating the resulting posterior probability distribution of interest to assess the considered model\\\\\\\'s network centrality measures. Experiments with synthetic and real-world stock price data are performed to validate the proposed algorithm\\\\\\\'s capabilities and show that this model has wider flexibility than the model proposed by [13].

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