The brain is a complex system, composed of multiple neural units interconnected at different spatial and temporal scales. Diffusion MRI allows probing in vivo the anatomical connectivity between different cortical areas through white matter tracts. In parallel, functional MRI records neural-related signals of brain activity. Particularly, during rest (in absence of specific external task) reproducible dynamical patterns of functional synchronization have been shown across different brain areas. This rich information can be conveniently represented in the form of a graph, a mathematical object where nodes correspond to cortical regions and are connected by edges representing anatomical connections. On the top of this structural network, or brain connectome, individual nodes are associated to functional signals representing neural activity over observation periods. Network science has fundamentally contributed to the characterization of the human connectome. The brain is a small-world network, able to combine segregation and integration aspects. These properties allow functional specialization on the one side, and efficient communication between distant brain areas on the other side, supporting complex cognitive and executive functions. Graph theoretical methods quantify brain topological properties, and allow their comparison between different populations and conditions. In fact, brain connectivity patterns and interdependences between anatomical substrate and functional synchronization have been proved to be impaired in a variety of brain disorders, and to change across human development and aging. Despite these important advancements in the understanding of the brain structure and functioning, many questions are currently unanswered. It is not clear for instance how structural connectivity features are related to individual cognitive capabilities and deficits, and if they have the concrete potential to distinguish pathological subgroups for early diagnosis of brain diseases. Most importantly, it is not yet understood how the connectome topology relates to specific brain functions, and how the transmission of information happens on the top of the structural connectivity infrastructure in order to generate observed functional dynamics. This thesis was motivated by these interdisciplinary inputs, and is the result of a strong interaction between biological and clinical questions on the one hand, and methodological development needs on the other hand. First, we have contributed to the characterization of the human connectome in health and pathologies by adapting and developing network measures for the description of the brain architecture at different scales. Particularly, we have focused on the topological characterization of subnetworks role within the overall brain network. Importantly, we have shown that the topological alteration of distinct brain subsystems may be a biomarker for different brain disorders. Second, we have proposed an original network model for the joint representation of brain structural and functional connectivity properties. This flexible spatio-temporal framework allows the investigation of functional dynamics at multiple temporal scales. Importantly, the investigation of spatio-temporal graphs in healthy subjects have allowed to disclose temporal relationships between local brain activations in resting state recordings, and has highlighted functional communication principles across the brain structural network.