Objective: In modern healthcare, accurately predicting diseases is a crucial matter. This study introduces a novel approach using graph neural networks (GNNs) and a Graph Transformer (GT) to predict the incidence of heart failure (HF) on a patient similarity graph at the next hospital visit. Materials and Methods: We used electronic health records (EHR) from the MIMIC-III dataset and applied the K-Nearest Neighbors (KNN) algorithm to create a patient similarity graph using embeddings from diagnoses, procedures, and medications. Three models - GraphSAGE, Graph Attention Network (GAT), and Graph Transformer (GT) - were implemented to predict HF incidence. Model performance was evaluated using F1 score, AUROC, and AUPRC metrics, and results were compared against baseline algorithms. An interpretability analysis was performed to understand the model's decision-making process. Results: The GT model demonstrated the best performance (F1 score: 0.5361, AUROC: 0.7925, AUPRC: 0.5168). Although the Random Forest (RF) baseline achieved a similar AUPRC value, the GT model offered enhanced interpretability due to the use of patient relationships in the graph structure. A joint analysis of attention weights, graph connectivity, and clinical features provided insight into model predictions across different classification groups. Discussion and Conclusion: Graph-based approaches such as GNNs provide an effective framework for predicting HF. By leveraging a patient similarity graph, GNNs can capture complex relationships in EHR data, potentially improving prediction accuracy and clinical interpretability.