How is the human brain structurally wired, and how is its activation functionally coordinated? Seeking the answer to this question is one of the great scientific challenges of the 21st century. The Human Connectome Project (HCP) is a project to construct a map of the complete structural and functional neural connections of the human brain. It is the first large-scale attempt to collect and share human brain imaging data at a scope and detail sufficient to begin addressing deeply fundamental questions about human connectional anatomy, within and across individuals. HCP database consists of a multiple MRI imaging acquisitions on a cohort of 1113 individuals. I seek to explore the structural and diffusion MRI acquisitions of this database based on the spectral graph theory schemes that I have been exploring in my PhD studies. The goal of the proposed project is to develop a detailed description of the brain topology and microstructure using novel graph encoding schemes. In particular, gray matter and white matter tissues of the brain are modeled as graphs, the former encoding the global topology of the cerebral cortex, and the latter encoding the convoluted structure of the underlying axonal tracts lying within white matter. The hypothesis is that characterizing the gray matter topology and white matter microstructure within the graph spectral domain can provide a more sensitive metric that can be exploited in longitudinal studies that aim to characterize neuroplasticity or brain structural atrophy in neurodegenerative disorders. Besides structural analysis, the aim is to also analyze the dynamics of the functional data from a spectral graph perspective. The hypothesis is that the spectral energy of the functional data should vary across tasks (7 different functional tasks) as well as across time in each task, and this spectral representation can open up new perspective in the functional organization of the brain.