In clinical artificial intelligence (AI), graph representation learning, mainly through graph neural networks (GNNs), stands out for its capability to capture intricate relationships within structured clinical datasets. With diverse data -- from patient records to imaging -- GNNs process data holistically by viewing modalities as nodes interconnected by their relationships. Graph AI facilitates model transfer across clinical tasks, enabling models to generalize across patient populations without additional parameters or minimal re-training. However, the importance of human-centered design and model interpretability in clinical decision-making cannot be overstated. Since graph AI models capture information through localized neural transformations defined on graph relationships, they offer both an opportunity and a challenge in elucidating model rationale. Knowledge graphs can enhance interpretability by aligning model-driven insights with medical knowledge. Emerging graph models integrate diverse data modalities through pre-training, facilitate interactive feedback loops, and foster human-AI collaboration, paving the way to clinically meaningful predictions.