Title: Learning Deep Generative Models of Graphs. Abstract: Graphs are fundamental data structures required to model many important real-world data, from knowledge graphs, physical and social interactions to molecules and proteins. In this paper, we study the problem of learning generative models of graphs from a dataset of graphs of interest. After learning, these models can be used to generate samples with similar properties as the ones in the dataset.  Such models can be useful in a lot of applications, e.g. drug discovery and knowledge graph construction. The task of learning generative models of graphs, however, has its unique challenges. In particular, how to handle symmetries in graphs and ordering of its elements during the generation process are important issues. We propose a generic graph neural net based model that is capable of generating any arbitrary graph.  We study its performance on a few graph generation tasks compared to baselines that exploit domain knowledge.  We discuss potential issues and open problems for such generative models going forward.