Balancing Efficiency and Expressiveness: Subgraph GNNs with Walk-Based Centrality

Joshua Southern, Yam Eitan, Guy Bar-Shalom, Michael M. Bronstein, Haggai Maron, Fabrizio Frasca

Keywords: Graph Neural Networks, Subgraph GNNs, Subgraphs, Expressive power

TL;DR: We propose a novel framework that uses walk-based centralities as a powerful Structural Encoding and to reduce the computational cost of Subgraph GNNs.

Abstract:

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.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 11932