Digital health apps have become a staple in daily life, promoting awareness and providing motivation for a healthier lifestyle. With an already overwhelmed healthcare system, digital therapies offer relief to both patient and physician alike. One such planned digital therapy application is the incorporation of an emotion recognition model as a tool for therapeutic interventions for people with autism spectrum disorder (ASD). Diagnoses of ASD have increased relatively rapidly in recent years. To ensure effective recognition of expressions, a system is designed to analyze and classify different emotions from facial landmarks. Facial landmarks combined with a corresponding mesh have the potential of bypassing hurdles of model robustness commonly affecting emotion recognition from images. Landmarks are extracted from facial images using the Mediapipe framework, after which a custom mesh is constructed from the detected landmarks and used as input to a graph convolution network (GCN) model for emotion classification. The GCN makes use of the relations formed from the mesh along with the special distance features extracted. A weighted loss approach is also utilized to reduce the effects of an imbalanced dataset. The model was trained and evaluated with the Aff-Wild2 database. The results yielded a 58.76% mean accuracy on the selected validation set. The proposed approach shows the potential and limitations of using GCNs for emotion recognition in real-world scenarios.