Graphon Cross-Validation: Assessing Models on Network Data

Graphon models have emerged as powerful tools for modeling complex network structures by capturing connection probabilities among nodes. A key challenge in their application lies in accurately characterizing the graphon function, particularly with respect to parameters that govern its smoothness, which significantly impact the estimation accuracy. In this article, we propose a novel graphon crossvalidation method for selecting tuning parameters and estimation approaches. Our method is both theoretically sound and computationally efficient. We show that our proposed cross-validation score is asymptotically parallel to the estimation error, and the selected model asymptotically converges to the optimal model. Through extensive simulations and real-world applications, we demonstrate that our method consistently delivers superior computational efficiency and accuracy.