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

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