Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classification

This paper challenges the theoretical foundations of Spectral Graph Neural Networks (GNNs), arguing they don't actually work as advertised for classifying nodes in graphs. The authors reveal that the mathematical 'frequency-domain filtering' these models claim to perform isn't theoretically sound, and their actual success comes from message-passing mechanics rather than spectral properties. They demonstrate that when spectral models are implemented correctly according to their design, they perform poorly—suggesting their reported effectiveness is due to implementation quirks that accidentally make them behave like simpler, non-spectral neural networks.