Meaningful division of the human cortex into distinct regions is a longstanding goal in neuroscience. Many of the most widely cited parcellations utilize anatomical priors or depend on functional magnetic resonance imaging (MRI) data while there exists a relative dearth of parcellations that use only structural data based on diffusion MRI. In light of this, and the fact that structural connectivity represents the underlying substrates of functional connectivity, we employ a novel high-resolution, vertex-level graph model of the whole-brain structural connectome and show that the harmonic modes of this graph can be used to achieve parcellations that qualitatively agree with the widely accepted atlases in the literature. Further, we detail a multi-layer formulation of the structural connectome graph and demonstrate that hierarchical clustering of its harmonic modes yields subject-specific parcellations at varying resolutions with ensured and tunable group-level correspondence.