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Streets networks provide an invaluable source of information about the different temporal and spatial patterns emerging in our cities. These streets are often represented as graphs where intersections are modelled as nodes and streets as links between them. Previous work has shown that raster representations of the original data can be created through a learning algorithm on low-dimensional representations of the street networks. In contrast, models that capture high-level urban network metrics can be trained through convolutional neural networks. However, the detailed topological data is lost through the rasterisation of the street network. The models cannot recover this information from the image alone, failing to capture complex street network features. This paper proposes a model capable of inferring good representations directly from the street network. Specifically, we use a variational autoencoder with graph convolutional layers and a decoder that outputs a probabilistic fully-connected graph to learn latent representations that encode both local network structure and the spatial distribution of nodes. We train the model on thousands of street network segments and use the learnt representations to generate synthetic street configurations. Finally, we proposed a possible application to classify the urban morphology of different network segments by investigating their common characteristics in the learnt space.