The PWLR Graph Representation: A Persistent Weisfeiler-Lehman scheme with Random Walks for Graph Classification

TL;DR

The paper introduces PWLR, a novel graph representation method combining Weisfeiler-Lehman, random walks, and persistent homology, which effectively captures local and global graph features for improved classification.

Contribution

It presents the PWLR scheme, a new mathematical framework that integrates multiple graph properties into explainable low-dimensional representations, generalizing existing Weisfeiler-Lehman variants.

Findings

Achieves classification performance comparable to state-of-the-art methods for graphs with discrete labels.

Enhances classification accuracy for graphs with continuous node features.

Provides explainable and stable graph representations against perturbations.

Abstract

This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs with discrete and continuous node features. The proposed scheme effectively incorporates normalized Weisfeiler-Lehman procedure, random walks on graphs, and persistent homology. We thereby integrate three distinct properties of graphs, which are local topological features, node degrees, and global topological invariants, while preserving stability from graph perturbations. This generalizes many variants of Weisfeiler-Lehman procedures, which are primarily used to embed graphs with discrete node labels. Empirical results suggest that these representations can be efficiently utilized to produce comparable results to state-of-the-art techniques in classifying graphs with discrete node labels, and enhanced performances in classifying those with continuous node features.