Is 3-(F)WL Enough to Distinguish All 3D Graphs?

Wanghan Xu

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arXiv · 2402.08429

Is 3-(F)WL Enough to Distinguish All 3D Graphs?

Wanghan Xu

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Abstract

The problem of graph isomorphism is an important but challenging problem in the field of graph analysis, for example: analyzing the similarity of two chemical molecules, or studying the expressive ability of graph neural networks. WL test is a method to judge whether two graphs are isomorphic, but it cannot distinguish all non-isomorphic graphs. As an improvement of WL, k-WL has stronger isomorphism discrimination ability, and as k increases, its discrimination ability is strictly increasing. However, whether the isomorphic discrimination power of k-WL is strictly increasing for more complex 3D graphs, or whether there exists k that can discriminate all 3D graphs, remains unexplored. This paper attempts to explore this problem from the perspective of graph generation.

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Wanghan Xu. 2024-01-24. Is 3-(F)WL Enough to Distinguish All 3D Graphs?. https://arxiv.org/abs/2402.08429

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