Maximally Expressive GNNs for Outerplanar Graphs

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

Keywords: expressive graph representation learning, outerplanar graphs

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.

Submission Number: 59