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.

提出了基于逐步 Weisfeiler-Lehman 随机游走方案（PWLR）的持久化算法，通过规范化的 Weisfeiler-Lehman 程序、图上随机游走和持久化同调等方法，将图的局部拓扑特征、节点度和全局拓扑不变量等特征结合起来，生成可解释的低维表示，该算法可以高效地分类带有离散或连续节点特征的图形，并取得可比较的结果。