Topology-constrained graph transformer network for structural and functional brain organization

The human brain exhibits a complex and hierarchical organization that supports efficient information integration across local and global scales. Accurately characterizing such topological organization from neuroimaging data remains challenging. Conventional graph neural networks (GNNs) effectively capture local dependencies through neighborhood aggregation but often overlook higher-order topological structures that reflect the brain's small-world organization. Although Transformer architectures enable global dependency modeling, their high computational cost limits scalability for large connected brain networks. To address these challenges, we propose a Topology-Constrained Graph Transformer Network (TC-GTN) that explicitly integrates brain network topology into graph learning. TC-GTN combines two complementary modules: a cycle-constrained graph convolution, which captures localized edge aggregation and models modular brain organization, and an MST-guided Transformer, which constrains global attention along minimum spanning tree (MST) pathways to efficiently model long-range dependencies while reducing redundant communication. Moreover, we introduce cycle-based edge positional encodings (CEPE) that provide a topological coordinate system for distinguishing edges with similar local structures but different cycle-level contexts. We evaluate TC-GTN on both structural and functional brain networks, extracted from diffusion-weighted imaging (DWI) and functional MRI (fMRI) respectively, using large-scale datasets, including UK Biobank (38557 participants; 18100 females/20457 males; age 40-70 years) and ABCD (7684 participants; 3782 females/3902 males; age 9-10 years). Experiments on sex classification and brain-age estimation demonstrate that TC-GTN consistently outperforms state-of-the-art graph network approaches, achieving superior accuracy, interpretability, and generalizability. Clinical significance analysis further demonstrates that the model accurately characterizes neuroanatomical divergence across pathological states. Using the brain age gap (BAG) as a biomarker, systemic accelerated aging is identified in multiple sclerosis and dementia, alongside heterogeneous structural alterations in stroke and Parkinson's disease. Our code is available at https://github.com/bieqa/TC-GTN.