The use of multiple drugs, termed polypharmacy, is common to treat patients with complex diseases or co-existing medical conditions. However, a major consequence of polypharmacy is a much higher risk of side effects for the patient. Polypharmacy side effects emerge because of drug interactions, in which activity of one drug may change, favorably or unfavorably, if taken with another drug. The knowledge of drug interactions is limited because these complex relationships are usually not observed in small clinical testing. Discovering polypharmacy side effects thus remains a challenge with significant implications for patient mortality and morbidity. Here we introduce Decagon, an approach for modeling polypharmacy side effects. The approach constructs a multimodal graph of protein-protein interactions, drug-protein interactions, and the polypharmacy side effects, which are represented as drug-drug interactions, where each side effect is an edge of a different type. Decagon is developed specifically to handle such multimodal graphs with a large number of edge types. Our approach develops a new graph convolutional neural network for multirelational link prediction in multimodal networks. Unlike approaches limited to predicting simple drug-drug interaction values, Decagon can predict the exact side effect, if any, through which a given drug combination manifests clinically. Decagon accurately predicts polypharmacy side effects, outperforming baselines by up to 69%. Furthermore, Decagon models particularly well side effects that have a strong molecular basis, while on predominantly non-molecular side effects, it achieves good performance because of effective sharing of model parameters across edge types. Decagon creates an opportunity to use large molecular and patient population data to flag and prioritize polypharmacy side effects for follow-up analysis via formal pharmacological studies.