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

Primary Area: learning on graphs and other geometries & topologies

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: expressive graph representation learning, outerplanar graphs

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

TL;DR: We propose a linear time graph transformation that enables the Weisfeiler-Leman (WL) test and message passing graph neural networks (MPNNs) to be maximally expressive on outerplanar graphs

Abstract: We propose a _linear time_ graph transformation that enables the Weisfeiler-Leman (WL) test 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.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 7232