Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be integrated for reliable graph clustering, especially in an unsupervised setting. However, existing methods based on shallow models often suffer from content noise and sparsity. In this work, we propose to utilize deep embedding for graph clustering, motivated by the well-recognized power of neural networks in learning intrinsic content representations. Upon that, we capture the dynamic nature of networks through the principle of influence propagation and calculate the dynamic network embedding. Network clusters are then detected based on the stable state of such an embedding. Unlike most existing embedding methods that are task-agnostic, we simultaneously solve for the underlying node representations and the optimal clustering assignments in an end-to-end manner. To provide more insight, we theoretically analyze our interpretation of network clusters and find its underlying connections with two widely applied approaches for network modeling. Extensive experimental results on six real-world datasets including both social networks and citation networks demonstrate the superiority of our proposed model over the state-of-the-art.