Although modern imaging technologies allow us to study connectivity between two distinct brain regions in-vivo, an in-depth understanding of how anatomical structure supports brain function and how spontaneous functional fluctuations support cognition is still elusive. Meanwhile, tremendous efforts have been made in the realm of machine learning to establish the nonlinear mapping between neuroimaging data and phenotypic traits. However, the absence of neuroscience insight in the current machine learning approaches poses significant challenges in understanding cognitive behavior from transient neural activities. To address this challenge, we put the spotlight on the coupling mechanism of structural connectivity (SC) and functional connectivity (FC) by reformulating this unresolved network neuroscience question into a graph representation learning problem for pathways. Specifically, we introduce the concept of topological detour to characterize how a ubiquitous instance of FC (direct link) is supported by neural pathways (detour) physically wired by SC, which forms a cyclic loop interacted by brain structure and function. The multi-hop detour pathway underlying SC-FC coupling allows us to devise a novel multi-head self-attention within a Transformer. Taken together, we propose a biological-inspired deep model, coined as NeuroDetour , to find putative connectomic feature representations from the unprecedented amount of neuroimaging data, which can be plugged into various downstream applications such as task recognition and disease diagnosis. We have evaluated NeuroDetour on large-scale public datasets including Human Connectome Project (HCP) and UK Biobank (UKB) under different experiment settings of supervised and zero-shot learning, where our NeuroDetour demonstrates state-of-the-art performance.