Title: The Infinite Contextual Graph Markov Model. Abstract: The Contextual Graph Markov Model is a deep, unsupervised, and probabilistic model for graphs that is trained incrementally on a layer-by-layer basis. As with most Deep Graph Networks, an inherent limitation is the lack of an automatic mechanism to choose the size of each layer's latent representation. In this paper, we circumvent the problem by extending the Contextual Graph Markov Model with Hierarchical Dirichlet Processes. The resulting model for graphs can automatically adjust the complexity of each layer without the need to perform an extensive model selection. To improve the scalability of the method, we introduce a novel approximated inference procedure that better deals with larger graph topologies. The quality of the learned unsupervised representations is then evaluated across a set of eight graph classification tasks, showing competitive performances against end-to-end supervised methods. The analysis is complemented by studies on the importance of depth, hyper-parameters, and compression of the graph embeddings. We believe this to be an important step towards the theoretically grounded and automatic construction of deep probabilistic architectures for graphs.