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 O(n^3) or O(n^4), making them computationally prohibitive for large graphs. In this paper, we start from the Original-DRESS equation (Castrillo, Leon, and Gomez, 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 Delta-DRESS, which runs DRESS on each node-deleted subgraph G\{v}, connecting the framework to the Kelly-Ulam reconstruction conjecture. Both Motif-DRESS and Delta-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 O(n^4) computational cost.

翻译：Weisfeiler-Lehman (WL) 层次结构是图同构测试与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，需要基于张量的运算，其复杂度高达O(n^3)或O(n^4)，这使得它们对于大规模图在计算上不可行。本文从Original-DRESS方程（Castrillo、Leon与Gomez，2018）——一个基于边的无参数连续动力系统——出发，证明了该方程能够区分棱柱图与K_{3,3}，而这对图是1-WL可证明无法区分的。接着，我们将其推广至Motif-DRESS，该方法将三角形邻域替换为任意结构模体，并在三个充分条件下收敛至唯一不动点；并进一步推广至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，我们提出了Delta-DRESS，它在每个节点删除子图G\{v}上运行DRESS，从而将该框架与Kelly-Ulam重构猜想联系起来。实验表明，Motif-DRESS与Delta-DRESS均能区分那些困扰3-WL的强正则图（SRGs），例如Rook图与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，在已知基准图上实验性地超越了1-WL和3-WL，同时避免了令人望而却步的O(n^4)计算成本。