Graph clustering has been a hot research topic and is widely used in many fields, such as community detection in social networks. Lots of works combining auto-encoder and graph neural networks have been applied to clustering tasks by utilizing node attributes and graph structure. These works usually assumed the inherent parameters (i.e. size and variance) of different clusters in the latent embedding space are homogeneous, and hence the assigned probability is monotonous over the Euclidean distance between node embeddings and centroids. Unfortunately, this assumption usually does not hold since the size and concentration of different clusters can be quite different, which limits the clustering accuracy. In addition, the node embeddings in deep graph clustering methods are usually L2 normalized so that it lies on the surface of a unit hyper-sphere. To solve this problem, we proposed D eep A daptive G raph C lustering via von Mises-Fisher distributions, namely DAGC. DAGC assumes the node embeddings H can be drawn from a von Mises-Fisher distribution and each cluster k is associated with cluster inherent parameters ρ _k which includes cluster center μ and cluster cohesion degree κ . Then we adopt an EM-like approach (i.e. \(\mathcal {P}(\mathbf {H}|\mathbf {ρ }) \) and \(\mathcal {P}(\mathbf {ρ }|\mathbf {H}) \) respectively) to learn the embedding and cluster inherent parameters alternately. Specifically, with the node embeddings, we proposed to update the cluster centers in an attraction-repulsion manner to make the cluster centers more separable. And given the cluster inherent parameters, a likelihood-based loss is proposed to make node embeddings more concentrated around cluster centers. Thus, DAGC can simultaneously improve the intra-cluster compactness and inter-cluster heterogeneity. Finally, extensive experiments conducted on four benchmark datasets have demonstrated that the proposed DAGC consistently outperforms the state-of-the-art methods, especially on imbalanced datasets.