Data-driven medical care delivery must always respect patient privacy-a requirement that is not easily met. This issue has impeded improvements to healthcare software and has delayed the long-predicted prevalence of artificial intelligence in healthcare. Until now, it has been very difficult to share data between healthcare organizations, resulting in poor statistical models due to unrepresentative patient cohorts. Synthetic data, i.e., artificial but realistic electronic health records, could overcome the drought that is troubling the healthcare sector. Deep neural network architectures, in particular, have shown an incredible ability to learn from complex data sets and generate large amounts of unseen data points with the same statistical properties as the training data. Here, we present a generative neural network model that can create synthetic health records with realistic timelines. These clinical trajectories are generated on a per-patient basis and are represented as linear-sequence graphs of clinical events over time. We use a variational graph autoencoder (VGAE) to generate synthetic samples from real-world electronic health records. Our approach generates health records not seen in the training data. We show that these artificial patient trajectories are realistic and preserve patient privacy and can therefore support the safe sharing of data across organizations.