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New Weisfeiler--Leman variant shows enhanced graph isomorphism testing power

By PulseAugur Editorial · [1 sources] ·

This paper introduces Implicit Line-Graph Higher-Order Weisfeiler--Leman (ILG-k-WL), a method for analyzing graph isomorphism by operating on the line graph relations derived from endpoint incidence without explicit construction. The research investigates the relationship between the expressivity of k-WL on line graphs and their root graphs, finding that for k=1,2, ILG-k-WL offers no additional distinguishing power. However, for k=3, ILG-3-WL demonstrates strictly greater expressivity than standard 3-WL, as evidenced by its ability to separate strongly regular witness pairs like the Shrikhande/rook pair. AI

IMPACT Introduces a novel theoretical framework for graph analysis, potentially impacting future research in graph neural networks and AI-driven pattern recognition.

RANK_REASON The cluster contains a single academic paper detailing a new theoretical framework for graph isomorphism testing. [lever_c_demoted from research: ic=1 ai=0.7]

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New Weisfeiler--Leman variant shows enhanced graph isomorphism testing power

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The cluster contains a single academic paper detailing a new theoretical framework for graph isomorphism testing. [lever_c_demoted from research: ic=1 ai=0.7]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Fan Yang ·

    On the Expressive Power of Implicit Line-Graph Higher-Order Weisfeiler--Leman

    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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