Assessing the critical view of safety in laparoscopic cholecystectomy requires accurate identification and localization of key anatomical structures, reasoning about their geometric relationships to one another, and determining the quality of their exposure. In this work, we propose to capture each of these aspects by modeling the surgical scene with a disentangled latent scene graph representation, which we can then process using a graph neural network. Unlike previous approaches using graph representations, we explicitly encode in our graphs semantic information such as object locations and shapes, class probabilities and visual features. We also incorporate an auxiliary image reconstruction objective to help train the latent graph representations. We demonstrate the value of these components through comprehensive ablation studies and achieve state-of-the-art results for critical view of safety prediction across multiple experimental settings.