Aiming for higher-level scene understanding, this work presents a neural network approach that takes a road-layout map in bird's-eye-view as input, and predicts a human-interpretable graph that represents the road's topological layout. Our approach elevates the understanding of road layouts from pixel level to the level of graphs. To achieve this goal, an image-graph-image auto-encoder is utilized. The network is designed to learn to regress the graph representation at its auto-encoder bottleneck. This learning is self-supervised by an image reconstruction loss, without needing any external manual annotations. We create a synthetic dataset containing common road layout patterns and use it for training of the auto-encoder in addition to the real-world Argoverse dataset. By using this additional synthetic dataset, which conceptually captures human knowledge of road layouts and makes this available to the network for training, we are able to stabilize and further improve the performance of topological road layout understanding on the real-world Argoverse dataset. The evaluation shows that our approach exhibits comparable performance to a strong fully-supervised baseline.