  Graph Neural Networks (GNNs) excel in diverse tasks, yet their applications
in high-stakes domains are often hampered by unreliable predictions. Although
numerous uncertainty quantification methods have been proposed to address this
limitation, they often lack \textit{rigorous} uncertainty estimates. This work
makes the first attempt to introduce a distribution-free and model-agnostic
uncertainty quantification approach to construct a predictive interval with a
statistical guarantee for GNN-based link prediction. We term it as
\textit{conformalized link prediction.} Our approach builds upon conformal
prediction (CP), a framework that promises to construct statistically robust
prediction sets or intervals. We first theoretically and empirically establish
a permutation invariance condition for the application of CP in link prediction
tasks, along with an exact test-time coverage. Leveraging the important
structural information in graphs, we then identify a novel and crucial
connection between a graph's adherence to the power law distribution and the
efficiency of CP. This insight leads to the development of a simple yet
effective sampling-based method to align the graph structure with a power law
distribution prior to the standard CP procedure. Extensive experiments
demonstrate that for conformalized link prediction, our approach achieves the
desired marginal coverage while significantly improving the efficiency of CP
compared to baseline methods.
