Resting-state functional magnetic resonance imaging (rs-fMRI) enables the characterization of functional interactions among distributed brain regions and has shown promise for brain disorder diagnosis. However, existing deep learning methods predominantly rely on node-centric representations, where brain regions serve as the primary learning units, potentially overlooking discriminative alterations embedded in functional connections. Here, we propose an edge-centric brain transformer (EBT) framework that reformulates rs-fMRI analysis as functional connection representation learning. Instead of modeling brain regions independently, EBT constructs edge time-series representations to capture dynamic co-fluctuation patterns of functional connections and organizes discriminative connections into a line graph for explicit connection-to-connection modeling. A structure-aware transformer is developed to learn both local dependencies among anatomically related connections and global interactions across distributed functional networks. Furthermore, an edge-level orthogonal clustering readout module is introduced to derive subject-level representations and identify latent connectivity modules associated with brain disorders. Evaluations on multiple neuroimaging datasets demonstrate that EBT consistently outperforms representative graph neural networks, brain transformers, and conventional connectivity-based approaches. Interpretability analyses further reveal stable disease-associated functional connections and connectivity modules that align with known pathological network alterations. These findings establish an edge-centric perspective for rs-fMRI-based brain disorder diagnosis and provide a promising framework for discovering interpretable connectivity biomarkers. The source code is publicly available at: https://github.com/Zdy12/Edge-centric-Brain-Transformer.

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