Deep generative models have been widely developed for graph data such as molecular graphs and point clouds. Yet, much less investigation has been carried out on understanding the learned latent space of deep graph generative models. Such understandings can open up a unified perspective and provide guidelines for essential tasks like controllable generation. To this end, this work develops a method called GraphCG for the unsupervised discovery of steerable factors in the latent space of deep graph generative models; GraphCG is able to steer key graph factors such as functional groups modification of molecules and engine updates in airplane point clouds. We first examine the representation space of the DGMs trained for graph and observe that the learned representation space is not perfectly disentangled. Based on this observation, GraphCG learns the semantic-rich directions via maximizing the corresponding mutual information, where the edited graph along the same direction will share certain steerable factors. We conduct experiments on two types of graph data, molecular graphs and point clouds. Both the quantitative and qualitative results show the effectiveness of GraphCG in discovering steerable factors.