This presentation introduces a conformal prediction methodology for quantifying uncertainty in populations of graph data. While existing literature offers numerous methods for graph prediction, techniques for assessing the uncertainty of these predictions remain scarce. The proposed framework addresses this gap by generating prediction regions for both labelled graphs, which possess a clear correspondence between nodes across observations, and unlabelled graphs, which lack such correspondence.

For unlabelled graphs, the methodology constructs prediction regions embedded within a discrete quotient metric space, referred to as graph space. The approach is model-free and does not rely on distributional assumptions. It achieves finite-sample validity and produces component-wise interpretable prediction regions configured as parallelotopes. Furthermore, the framework incorporates a length modulation mechanism to account for the local variability of specific edge or node attributes.

The theoretical properties and empirical performance of this forecasting technique are evaluated through two simulation studies covering both labelled and unlabelled graph scenarios. Additionally, the practical utility of the method is demonstrated using a real-world dataset of player passing networks from the FIFA 2018 World Cup. This application illustrates the framework's capacity to analyze network topology and quantify prediction uncertainty for football teams categorized by varying performance levels.