Maximally Expressive GNNs for Outerplanar Graphs

Franka Bause, Fabian Jogl, Patrick Indri, Tamara Drucks, David Penz, Nils Morten Kriege, Thomas Gärtner, Pascal Welke, Maximilian Thiessen

Abstract: We propose a linear time graph transformation that enables the Weisfeiler-Leman (WL) algorithm and message passing graph neural networks (MPNNs) to be maximally expressive on outerplanar graphs. Our approach is motivated by the fact that most pharmaceutical molecules correspond to outerplanar graphs. Existing research predominantly enhances the expressivity of graph neural networks without specific graph families in mind. This often leads to methods that are impractical due to their computational complexity. In contrast, the restriction to outerplanar graphs enables us to encode the Hamiltonian cycle of each biconnected component in linear time. As the main contribution of the paper we prove that our method achieves maximum expressivity on outerplanar graphs. Experiments confirm that our graph transformation improves the predictive performance of MPNNs on molecular benchmark datasets at negligible computational overhead.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission: We have incorporated the reviewers' suggestions as outlined in the rebuttal. In particular, we revised the introduction to better clarify the relationship between expressivity and model performance. Additionally, we provided more examples of the CAT* transformation and further explanations for the definition of CAT. An extensive explanation of the definition of outerplanar graphs has been added to the appendix, and we have included more detailed descriptions of both the implementation and experimental setup.

Video: https://www.youtube.com/watch?v=AW6Cy6pcc1Y

Code: https://github.com/ocatias/outerplanarGNN

Assigned Action Editor: ~Ellen_Vitercik1

Submission Number: 3089