The graph structure can reveal the relationships between feature nodes and improve the performance of feature-based models. However, more research is needed to construct a patient graph representation using electronic medical record (EMR) to meet modeling requirements. This study aims to propose a heterogeneous patient graph representation (HePGR) framework capable of discovering associations between medical concepts in EMR while simultaneously supporting both clustering and classification tasks. We construct HePGR's edge connections by evaluating the correlations between medical concepts(e.g., laboratory tests, drugs, surgical codes) using positive pointwise mutual information, directly linking patients with their corresponding medical concepts. Graph attention networks are used to obtain patient node representations, with a supervised training method based on cross-entropy and a semi-supervised method leveraging pseudo-labeling and contrastive learning. To validate the effectiveness of the HePGR model, we design comparison and ablation experiments that are performed on a stroke patient dataset with two prediction tasks and one clustering task. HePGR shows superior performance in all tasks, achieving areas under the receiver operating characteristic curve of 0.990 and 0.806 in the two prediction tasks and a Jaccard coefficient of 0.810 in the clustering task. The proposed HePGR model effectively identifies associations between medical concepts and shows high performance in clinical tasks. This model is expected to be extended to more medical concepts for broad clinical applicability.