Maximally Expressive GNNs for Outerplanar Graphs

Abstract

Most pharmaceutical molecules can be represented as outerplanar graphs. We propose a graph transformation that makes the Weisfeiler-Leman (WL) test and message passing graph neural networks maximally expressive on outerplanar graphs. While existing research predominantly focuses on enhancing expressivity of graph neural networks beyond the WL test on arbitrary graphs, our goal is to distinguish pharmaceutical graphs specifically. Our approach applies a linear time transformation, building on the fact that biconnected outerplanar graphs can be uniquely identified by their Hamiltonian adjacency list sequences. This pre-processing step can then be followed by any graph neural network. We achieve promising results on molecular benchmark datasets while keeping the pre-processing time low, in the order of seconds for common benchmarks.