Patients needing emergency department (ED) services are sorted into urgency categories using triage, often through severity indexes like the Emergency Severity Index (ESI), traditionally done manually by nurses. This study introduces a network-based patient modelling approach using Graph Neural Networks (GNNs) to automate triage by leveraging inter-patient similarities and inter-feature relationships. The method employs two models: one that views patients as nodes in a similarity graph (Patient-Level modelling), and another that forms a graph for each patient where nodes represent features connected based on mutual information (Feature-Level modelling). The findings confirm the effectiveness of these methods and their potential to improve triage accuracy, with future possibilities for enhancing transparency and clinical applicability through explainability techniques.