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Resting-state functional magnetic resonance imaging (rs-fMRI) provides a non-invasive solution to explore abnormal brain connectivity patterns caused by brain disorders. Graph neural network (GNN) has been widely used for fMRI representation learning and brain disorder analysis, thanks to its potent graph representation abilities. Training a generalizable GNN model often requires large-scale subjects from different medical centers/sites, but the traditional centralized utilization of multi-site data unavoidably encounters challenges related to data privacy and storage. Federated learning (FL) can coordinate multiple sites to train a shared model without centrally integrating multi-site fMRI data. However, previous FL-based methods for fMRI analysis usually ignore specificity of each site, including factors such as age, gender, and population. To this end, we propose a specificity-aware federated graph learning (SFGL …