Semantic maps are a means of representing universal structure underlying crosslanguage semantic variation. However, no algorithm has existed for inferring a graph-based semantic map from data. Here, we note that this open problem is formally identical to the known problem of inferring a social network from disease outbreaks. From this identity it follows that semantic map inference is computationally intractable, but that an efficient approximation algorithm for it exists. We demonstrate that this algorithm produces sensible semantic maps from two existing bodies of data. We conclude that universal semantic graph structure can be automatically approximated from cross-language semantic data.