The network graph visualizes patient relationships using force-directed layout, where nodes represent individual patients from the dataset and links show connections between them. The visualization is rendered as SVG in a React framework using d3.v7, with d3.forceSimulation handling the physics-based positioning and collision detection. The graph displays patient attributes such as age, gender, and race through node styling, with interactive zoom and pan capabilities enabled through d3.zoom. The code uses d3.select and .join() to manage the SVG elements dynamically based on state changes.