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

arXiv: https://arxiv.org/abs/2402.08429 · HTML: https://mlsanity.com/paper/2402.08429/

## Key facts

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- First posted on arXiv 24 Jan 2024.

## Abstract (arXiv)

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.