Abstract As a fundamental machine learning problem, graph clustering has facilitated various real-world applications, and tremendous efforts had been devoted to it in the past few decades. However, most of the existing methods like spectral clustering suffer from the sparsity, scalability, robustness and handling high dimensional raw information in clustering. To address this issue, we propose a deep probabilistic model, called Variational Graph Embedding and Clustering with Laplacian Eigenmaps (VGECLE), which learns node embeddings and assigns node clusters simultaneously. It represents each node as a Gaussian distribution to disentangle the true embedding position and the uncertainty from the graph. With a Mixture of Gaussian (MoG) prior, VGECLE is capable of learning an interpretable clustering by the variational inference and generative process. In order to learn the pairwise relationships better, we propose a Teacher-Student mechanism encouraging node to learn a better Gaussian from its instant neighbors in the stochastic gradient descent (SGD) training fashion. By optimizing the graph embedding and the graph clustering problem as a whole, our model can fully take the advantages in their correlation. To our best knowledge, we are the first to tackle graph clustering in a deep probabilistic viewpoint. We perform extensive experiments on both synthetic and real-world networks to corroborate the effectiveness and efficiency of the proposed framework