We proposed a novel framework to learn graph structure from unlabeled data. This approach can accurately learn a graph structure, which can then be used by graph-based event detection methods such as GraphScan, enabling more timely and accurate detection of outbreaks, which spread based on that latent structure. Our results show that the learned graph structure is similar to the true underlying graph structure. The resulting graph often has better detection power than the true graph, enabling more timely detection of outbreaks, while achieving similar spatial accuracy to the true graph.