Most analyses on functional brain connectivity across a group of brains are under the assumption that the positions of the voxels are aligned into a common space. However, the alignment errors are inevitable. To address this issue, the distributional representation avoids the alignment in such a way that the spatial structure of connectivity is captured by the distance between voxels to preserve the relative position information. Unlike other relevant connectivity analyses that only consider connections with higher correlation values between voxels, the distributional approach takes the whole picture. It can find outliers visually in a large dataset. The centroid of a group of brains and the orbit of brains around their categorical centroid are discovered, on a basis of which a clear boundary appears between a disordered category and the control group in a distributional representation space. Moreover, it can guide correlation threshold selection for conventional brain network analysis. In contrast to the main-stream representation such as selected network properties for disease classification, the distributional representation is task-free, which provides a promising foundation for further analysis on functional brain connectivity in various ends.