Electronic Medical Records (EHR) are extremely sparse. Only a small proportion of events (symptoms, diagnoses, and treatments) are observed in the lifetime of an individual. The high degree of missingness of EHR can be attributed to a large number of factors, including device failure, privacy concerns, or other unexpected reasons. Unfortunately, many traditional imputation methods are not well suited for highly sparse data and scale poorly to high dimensional datasets. In this paper, we propose a graph-based imputation method that is both robust to sparsity and to unreliable unmeasured events. Our approach compares favourably to several standard and state-of-the-art imputation methods in terms of performance and runtime. Moreover, results indicate that the model learns to embed different event types in a clinically meaningful way. Our work can facilitate the diagnosis of novel diseases based on the clinical history of past events, with the potential to increase our understanding of the landscape of comorbidities.