The Weisfeiler-Lehman (WL) hierarchy is a cornerstone framework for graph isomorphism testing and structural analysis. However, scaling beyond 1-WL to 3-WL and higher requires tensor-based operations that scale as $\mathcal{O}(n^3)$ or $\mathcal{O}(n^4)$, making them computationally prohibitive for large graphs. In this paper, we start from the Original-DRESS equation (Castrillo, León, and Gómez, 2018) -- a parameter-free, continuous dynamical system on edges -- and show that it distinguishes the prism graph from $K_{3,3}$, a pair that 1-WL provably cannot separate. We then generalize it to Motif-DRESS, which replaces triangle neighborhoods with arbitrary structural motifs and converges to a unique fixed point under three sufficient conditions, and further to Generalized-DRESS, an abstract template parameterized by the choice of neighborhood operator, aggregation function and norm. Finally, we introduce $Δ$-DRESS, which runs DRESS on each node-deleted subgraph $G \setminus \{v\}$, connecting the framework to the Kelly--Ulam reconstruction conjecture. Both Motif-DRESS and $Δ$-DRESS empirically distinguish Strongly Regular Graphs (SRGs) -- such as the Rook and Shrikhande graphs -- that confound 3-WL. Our results establish the DRESS family as a highly scalable framework that empirically surpasses both 1-WL and 3-WL on well-known benchmark graphs, without the prohibitive $\mathcal{O}(n^4)$ computational cost.

翻译：Weisfeiler-Lehman (WL) 层次结构是图同构测试和结构分析的基石框架。然而，将尺度从 1-WL 扩展到 3-WL 及更高阶，需要基于张量的操作，其计算复杂度为 $\mathcal{O}(n^3)$ 或 $\mathcal{O}(n^4)$，这使得它们对于大型图在计算上不可行。本文从 Original-DRESS 方程（Castrillo, León, and Gómez, 2018）——一个在边上的无参数连续动力系统——出发，证明了它能够区分棱柱图和 $K_{3,3}$，而这对图是 1-WL 可证明无法区分的。接着，我们将其推广到 Motif-DRESS，它用任意的结构模体取代三角形邻域，并在三个充分条件下收敛到唯一的固定点；并进一步推广到 Generalized-DRESS，这是一个由邻域算子、聚合函数和范数选择参数化的抽象模板。最后，我们引入了 $Δ$-DRESS，它在每个节点删除子图 $G \setminus \{v\}$ 上运行 DRESS，从而将该框架与 Kelly--Ulam 重构猜想联系起来。Motif-DRESS 和 $Δ$-DRESS 在实验上均能区分那些困扰 3-WL 的强正则图（SRGs）——例如 Rook 图和 Shrikhande 图。我们的研究结果确立了 DRESS 系列作为一个高度可扩展的框架，在著名的基准图上，其经验性能超越了 1-WL 和 3-WL，同时避免了 $\mathcal{O}(n^4)$ 的过高计算成本。