Paper
DRESS: A Continuous Framework for Structural Graph Refinement
Authors
Eduar Castrillo Velilla
Abstract
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.20833v1</id>\n <title>DRESS: A Continuous Framework for Structural Graph Refinement</title>\n <updated>2026-02-24T12:18:42Z</updated>\n <link href='https://arxiv.org/abs/2602.20833v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.20833v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.DS'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <published>2026-02-24T12:18:42Z</published>\n <arxiv:primary_category term='cs.DS'/>\n <author>\n <name>Eduar Castrillo Velilla</name>\n </author>\n </entry>"
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