Logical Expressiveness of Graph Neural Networks with Hierarchical Node Individualization

TL;DR

This paper introduces Hierarchical Ego Graph Neural Networks (HEGNNs), a new class of GNNs with hierarchical node individualization that can distinguish graphs up to isomorphism and outperform traditional GNNs in experiments.

Contribution

The paper proposes HEGNNs, a novel hierarchical GNN model that generalizes existing methods and achieves maximum expressive power for graph isomorphism testing.

Findings

HEGNNs match the distinguishing power of graded hybrid logic on bounded degree graphs.

HEGNNs outperform traditional GNNs in practical experiments.

HEGNNs are feasible and beneficial compared to existing GNN architectures.

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 isomorphism testing. HEGNNs 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 HEGNN node classifiers equals that of 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.