Benchmarking Spectral Graph Neural Networks: A Comprehensive Study on Effectiveness and Efficiency

With the recent advancements in graph neural networks (GNNs), spectral GNNs have received increasing popularity by virtue of their specialty in capturing graph signals in the frequency domain, demonstrating promising capability in specific tasks. However, few systematic studies have been conducted on assessing their spectral characteristics. This emerging family of models also varies in terms of designs and settings, leading to difficulties in comparing their performance and deciding on the suitable model for specific scenarios, especially for large-scale tasks. In this work, we extensively benchmark spectral GNNs with a focus on the frequency perspective. We analyze and categorize over 30 GNNs with 27 corresponding filters. Then, we implement these spectral models under a unified framework with dedicated graph computations and efficient training schemes. Thorough experiments are conducted on the spectral models with inclusive metrics on effectiveness and efficiency, offering practical guidelines on evaluating and selecting spectral GNNs with desirable performance. Our implementation enables application on larger graphs with comparable performance and less overhead, which is available at: https://github.com/gdmnl/Spectral-GNN-Benchmark.