A Novel Graph Distance Method Combining Optimal Transport and WL Subtrees

Abstract

In this work, we introduce a novel graph distance that combines optimal transport and Weisfeiler-Lehman (WL) subtrees. Unlike conventional graph metrics of the WL series, which focus on graph consistency, our proposed graph distance can capture structural differences between graphs. We show that our method outperforms baselines in both metric validation and graph classification experiments, demonstrating that it can overcome the limitations of existing WL-based graph metrics.