The structural connectome is often represented by fiber bundles generated\nfrom various types of tractography. We propose a method of analyzing\nconnectomes by representing them as a Riemannian metric, thereby viewing them\nas points in an infinite-dimensional manifold. After equipping this space with\na natural metric structure, the Ebin metric, we apply object-oriented\nstatistical analysis to define an atlas as the Fr\\'echet mean of a population\nof Riemannian metrics. We demonstrate connectome registration and atlas\nformation using connectomes derived from diffusion tensors estimated from a\nsubset of subjects from the Human Connectome Project.\n