  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.
