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

TL;DR

This paper introduces HyMN, a walk-based centrality sampling method that significantly reduces the computational cost of Subgraph GNNs, enabling their application to larger graphs while maintaining high performance.

Contribution

We propose HyMN, a novel, simple, and efficient approach using walk-based centrality measures to sample relevant subgraphs, improving scalability and discriminative power of Subgraph GNNs.

Findings

HyMN reduces subgraph bag size and computational cost.

HyMN outperforms existing sampling methods in efficiency and accuracy.

HyMN enables application of Subgraph GNNs to larger graphs.

Abstract

Subgraph GNNs have emerged as promising architectures that overcome the expressiveness limitations of Graph Neural Networks (GNNs) by processing bags of subgraphs. Despite their compelling empirical performance, these methods are afflicted by a high computational complexity: they process bags whose size grows linearly in the number of nodes, hindering their applicability to larger graphs. In this work, we propose an effective and easy-to-implement approach to dramatically alleviate the computational cost of Subgraph GNNs and unleash broader applications thereof. Our method, dubbed HyMN, leverages walk-based centrality measures to sample a small number of relevant subgraphs and drastically reduce the bag size. By drawing a connection to perturbation analysis, we highlight the strength of the proposed centrality-based subgraph sampling, and further prove that these walk-based centralities can be additionally used as Structural Encodings for improved discriminative power. A comprehensive set of experimental results demonstrates that HyMN provides an effective synthesis of expressiveness, efficiency, and downstream performance, unlocking the application of Subgraph GNNs to dramatically larger graphs. Not only does our method outperform more sophisticated subgraph sampling approaches, it is also competitive, and sometimes better, than other state-of-the-art approaches for a fraction of their runtime.