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.

翻译：本文提出并研究了层次化自我图神经网络（HEGNNs），这是一种受同构测试中个性化-精化范式启发、具有层次化节点个性化能力的图神经网络（GNNs）的扩展模型，具有更强的表达能力。HEGNNs 泛化了子图-GNNs，并形成了一个表达能力逐级增强的模型层次结构，在极限情况下能够区分非同构图。我们证明，在有界度图上，HEGNNs 节点分类器的区分能力等价于分级混合逻辑的区分能力。这一特征刻画使我们能够将 HEGNNs 的区分能力与高阶 GNNs、通过局部同态计数特征增强的 GNNs，以及基于个性化-精化的颜色精化算法进行比较。我们的实验结果证实了 HEGNNs 的实际可行性，并展示了其与传统 GNN 架构（无论是否包含局部同态计数特征）相比的优势。