Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization

• URL: http://arxiv.org/abs/2506.13911v1
• Date: Mon, 16 Jun 2025 18:39:31 GMT
• Title: Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization
• Authors: Arie Soeteman, Balder ten Cate,
• Abstract summary: Hierarchical Ego Graph Neural Networks (HEGNNs) are an expressive extension of graph neural networks (GNNs)<n>HEGNNs generalize subgraph-GNNs and form a hierarchy of increasingly expressive models that can distinguish graphs up to isomorphism.<n>Our experimental results confirm the practical feasibility of HEGNNs and show benefits in comparison with traditional GNN architectures.
• Score: 0.6215404942415159
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose and study Hierarchical Ego Graph Neural Networks (HEGNNs), an expressive extension of graph neural networks (GNNs) with hierarchical node individualization, inspired by the Individualization-Refinement paradigm for graph isomorphism testing. HEGNNs generalize subgraph-GNNs and form a hierarchy of increasingly expressive models that, in the limit, can distinguish graphs up to isomorphism. We provide a logical characterization of HEGNN node classifiers, with and without subgraph restrictions, using graded hybrid logic. This characterization enables us to relate the separating power of HEGNNs 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 HEGNNs and show benefits in comparison with traditional GNN architectures, both with and without local homomorphism count features.

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