We propose an expressive and efficient approach that combines the strengths of two prominent extensions of Graph Neural Networks (GNNs): Subgraph GNNs and Structural Encodings (SEs). Our approach leverages walk-based centrality measures, both as a powerful form of SE and also as a subgraph selection strategy for Subgraph GNNs. By drawing a connection to perturbation analysis, we highlight the effectiveness of centrality-based sampling, and show it significantly reduces the computational burden associated with Subgraph GNNs. Further, we combine our efficient Subgraph GNN with SEs derived from the calculated centrality and demonstrate this hybrid approach, dubbed HyMN, gains in discriminative power. HyMN effectively addresses the expressiveness limitations of Message Passing Neural Networks (MPNNs) while mitigating the computational costs of Subgraph GNNs. Through a series of experiments on synthetic and real-world tasks, we show it outperforms other subgraph sampling approaches while being competitive with full-bag Subgraph GNNs and other state-of-the-art approaches with a notably reduced runtime.

翻译：我们提出了一种兼具表达能力与效率的方法，该方法融合了图神经网络（GNNs）两种重要扩展——子图GNNs与结构编码（SEs）——的优势。我们的方法利用基于行走的中心性度量，既作为一种强大的SE形式，也作为子图GNNs的子图选择策略。通过建立与扰动分析的联系，我们强调了基于中心性采样的有效性，并证明它能显著减轻子图GNNs相关的计算负担。此外，我们将我们高效的子图GNN与从计算所得中心性导出的SEs相结合，并证明这种混合方法（命名为HyMN）在判别能力上有所提升。HyMN有效解决了消息传递神经网络（MPNNs）的表达能力局限，同时缓解了子图GNNs的计算成本。通过对合成任务和现实世界任务的一系列实验，我们证明它在显著减少运行时间的同时，性能优于其他子图采样方法，并与全袋子图GNNs及其他最先进方法具有竞争力。