Topology-Aware Neural Collapse for Generalized Category Discovery on Graphs

Learning a stable yet highly discriminative representation space that can simultaneously recognize known categories and discover novel ones from limited labeled data is fundamental to Generalized Category Discovery (GCD) on graphs. Recently, Neural Collapse (NC) theory has emerged as a powerful geometric principle for GCD, yielding maximally separated and well-structured class representations by encouraging feature embeddings to converge toward Simplex Equiangular Tight Frame (Simplex ETF) prototypes. However, when extending this paradigm to graph-structured data, a critical challenge arises. Graph representations are inherently shaped by topological dependencies, where neighborhood-based message passing enforces local smoothness among connected nodes. This topology-induced smoothing conflicts with the strict geometric convergence required by Simplex ETF, making neural collapse difficult to realize on graphs. To address this issue, we propose TopoNC, a topology-aware neural collapse framework for Graph GCD. Specifically, it fixes Simplex ETF prototypes as global geometric targets and introduces a Dual-Stream Encoder that decouples topology smoothing from feature-discriminative learning, adaptively balancing the two streams via a gating mechanism. In addition, we further design a Topology-Conditioned Pseudo-Labeling strategy that integrates Sinkhorn-based global balancing, Old-Class Top-K Admission Masking, and Neighborhood-Consensus Screening, to reliably guide feature collapse. Extensive experiments on several benchmark datasets have demonstrated that TopoNC consistently outperforms existing methods, highlighting the importance of topology-aware neural collapse for Graph GCD.