Beyond Weisfeiler-Lehman with Local Ego-Network Encodings

Nurudin Alvarez-Gonzalez, Andreas Kaltenbrunner, Vicenç Gómez

Abstract: Identifying similar network structures is key to capturing graph isomorphisms and learning representations that exploit structural information encoded in graph data. This work shows that ego networks can produce a structural encoding scheme for arbitrary graphs with greater expressivity than the Weisfeiler–Lehman (1-WL) test. We introduce I G E L , a preprocessing step to produce features that augment node representations by encoding ego networks into sparse vectors that enrich message passing (MP) graph neural networks (GNNs) beyond 1-WL expressivity. We formally describe the relation between I G E L and 1-WL, and characterize its expressive power and limitations. Experiments show that I G E L matches the empirical expressivity of state-of-the-art methods on isomorphism detection while improving performance on nine GNN architectures and six graph machine learning tasks.