Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization

Arie Soeteman, Balder ten Cate

Advances in Neural Information Processing Systems 38 (NeurIPS 2025) Main Conference Track

We propose and study Hierarchical Ego Graph Neural Networks (HE-GNNs), an expressive extension of graph neural networks (GNNs) with hierarchical node individualization, inspired by the Individualization-Refinement paradigm for isomorphism testing. HE-GNNs generalize subgraph-GNNs and form a hierarchy of increasingly expressive models that, in the limit, distinguish graphs up to isomorphism. We show that, over graphs of bounded degree, the separating power of HE-GNN node classifiers equals that of graded hybrid logic. This characterization enables us to relate the separating power of HE-GNNs to that of higher-order GNNs, GNNs enriched with local homomorphism count features, and color refinement algorithms based on Individualization-Refinement. Our experimental results confirm the practical feasibility of HE-GNNs and show benefits in comparison with traditional GNN architectures, both with and without local homomorphism count features.