Wasserstein Graph Distance Based on $L_1$-Approximated Tree Edit Distance between Weisfeiler-Lehman Subtrees

TL;DR

This paper introduces the WWLS distance, a new graph metric combining Wasserstein distance and $L_1$-approximated tree edit distance, to better detect subtle structural differences in graphs, improving over existing methods.

Contribution

The paper proposes the WWLS distance, a novel graph metric that captures slight structural differences by integrating WL subtrees with $L_1$-TED and Wasserstein distance.

Findings

WWLS outperforms baseline metrics in graph classification.

The method effectively detects subtle structural differences.

Experimental validation confirms improved metric sensitivity.

Abstract

The Weisfeiler-Lehman (WL) test is a widely used algorithm in graph machine learning, including graph kernels, graph metrics, and graph neural networks. However, it focuses only on the consistency of the graph, which means that it is unable to detect slight structural differences. Consequently, this limits its ability to capture structural information, which also limits the performance of existing models that rely on the WL test. This limitation is particularly severe for traditional metrics defined by the WL test, which cannot precisely capture slight structural differences. In this paper, we propose a novel graph metric called the Wasserstein WL Subtree (WWLS) distance to address this problem. Our approach leverages the WL subtree as structural information for node neighborhoods and defines node metrics using the $L_1$-approximated tree edit distance ($L_1$-TED) between WL subtrees of nodes. Subsequently, we combine the Wasserstein distance and the $L_1$-TED to define the WWLS distance, which can capture slight structural differences that may be difficult to detect using conventional metrics. We demonstrate that the proposed WWLS distance outperforms baselines in both metric validation and graph classification experiments.