English(EN) On the Expressive Power of Implicit Line-Graph Higher-Order Weisfeiler--Leman

新的 Weisfeiler--Leman 变体显示出增强的图同构测试能力

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-16 04:00

本文介绍了隐式线图高阶 Weisfeiler--Leman (ILG-k-WL)，一种通过操作源自端点关联的线图关系而不进行显式构建来分析图同构的方法。研究探讨了 k-WL 在线图上的表达能力与其根图之间的关系，发现对于 k=1,2，ILG-k-WL 不提供额外的区分能力。然而，对于 k=3，ILG-3-WL 表现出比标准 3-WL 更强的表达能力，这可以通过它区分 Shrikhande/rook 对等强正则对的能力来证明。 AI

影响引入了图分析的新颖理论框架，可能影响图神经网络和人工智能驱动的模式识别的未来研究。

排序理由该集群包含一篇关于图同构测试新理论框架的学术论文。[lever_c_demoted from research: ic=1 ai=0.7]

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arXiv cs.AI TIER_1 English(EN) · Fan Yang · 2026-09-16 04:00

关于隐式线图高阶Weisfeiler--Leman的表达能力

arXiv:2609.16412v1 Announce Type: cross Abstract: Whitney's theorem allows isomorphism testing for connected simple graphs, apart from $K_3$ and $K_{1,3}$, to be formulated as distinguishing their line graphs. However, the relation between fixed-dimensional Weisfeiler--Leman (WL)…

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关于隐式线图高阶Weisfeiler--Leman的表达能力

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