Non-invasive characterization of brain structure has been made possible by the introduction of magnetic resonance imaging (MRI). Graph modeling of structural connectivity has been useful, but is often limited to defining nodes as regions from a brain atlas. Here, we propose two methods for encoding structural connectivity in a huge brain graph at the voxel-level resolution (i.e., 850'000 voxels) based on diffusion tensor imaging (DTI) and the orientation density functions (ODF), respectively. The eigendecomposition of the brain graph's Laplacian operator is then showing highly resolved eigenmodes that reflect distributed structural features which are in good correspondence with major white matter tracks. To investigate the intrinsic dimensionality of eigenspace across subjects, we used a Procrustes validation that characterizes inter-subject variability. We found that the ODF approach using 3-neighborhood captures the most information from the diffusion-weighted MRI. The proposed methods open a wide range of possibilities for new research avenues, especially in the field of graph signal processing applied to functional brain imaging.