The Isomorphism Trap: Rethinking Expressive Power for Graph Node Classification

The dominant view of Graph Neural Network (GNN) expressive power is grounded in the Weisfeiler--Lehman (WL) graph isomorphism framework, motivating the development of architectures with increasingly strong isomorphism-discrimination capabilities. We argue that this perspective is problematic for graph node classification. First, when node features are heterogeneous, WL refinement no longer acts as a purely structural discriminator because feature information becomes entangled with topology. Second, structural distinguishability is neither necessary nor sufficient for correct classification: structurally equivalent nodes may require different labels, while structurally distinct nodes may share the same label. Third, even in topology-critical tasks, message passing implements a diffusion process constrained by graph structure rather than a procedure for isomorphism discrimination, so what such tasks require is sensitivity to structure or structure-feature interaction, not the capacity to distinguish non-isomorphic nodes. We therefore argue that isomorphism-testing ability is an inappropriate primary measure of GNN expressive power for node classification, and that future analyses should focus on task-relevant interactions between features, structure, and prediction objectives.