Title: GraphCG: Unsupervised Discovery of Steerable Factors in Graphs. Abstract: 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 unsupervised discovery of steerable factors in latent space of deep graph generative models. We first examine the representation space of the recent deep generative models trained for graph data, and observe that the learned representation space is not perfectly disentangled. Thus, our method is designed for discovering steerable factors of graph data in a model-agnostic and task-agnostic manner. Specifically, GraphCG learns the semantic-rich directions via maximizing the corresponding mutual information, where the edited graph along the same direction will possess 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 for discovering steerable factors.