In recent years developments in graph theoretical analysis have been more and more applied to the study and characterization of both functional and structural brain networks. The human connectome has been characterized as a small-world, modular, hierarchical network, with few central nodes acting as connectors between local communities, and highly interconnected between them. This brain characterization is common to both structural and functional connectivity. Nevertheless the correlation between the two has not yet been clearly uncovered. My PhD research includes the characterization and formalism of the structure-function relationship, and the application of traditional and new methods to the investigation of schizophrenia and early stage of psychosis. This project is in collaboration with the Centre hospitalier universitaire vaudois (CHUV). I am contributing developer of the Connectome Mapper (http://www.cmtk.org), an open-source, Python-based software for diffusion MRI data processing and brain connectomes construction.