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Mining patterns in graphs has become an important issue in real applications, such as bioinformatics and web mining. We address a graph clustering problem where a cluster is a set of densely connected nodes, under a practical setting that 1) the input is multiple graphs which share a set of nodes but have different edges and 2) a true cluster cannot be found in all given graphs. For this problem, we propose a probabilistic generative model and a robust learning scheme based on variational Bayesian estimation. A key feature of our probabilistic framework is that not only nodes but also given graphs can be clustered at the same time, allowing our model to capture clusters found in only part of all given graphs. We empirically evaluated the effectiveness of the proposed framework on not only a variety of synthetic graphs but also real gene networks, demonstrating that our proposed approach can improve the clustering performance of competing methods in both synthetic and real data.