Ricerca di una partizione nascosta e comune nelle reti cerebrali a due strati struttura-funzione.

The aim of this thesis is to investigate the intricate relationship between brain structure and function with complex networks analysis tools. Several works in neuroimaging indicate the presence of robust partitions in both structural (SC) and resting state functional networks (rsFC), confirming that these two networks are correlated. The function acts on the structure in virtue of the mechanism of neural plasticity, and conversely the structure acts on the function by means of topological constraints. In the attempt to understand this relationship, we focus on group of nodes making a comparison among structural and functional networks by exploiting their hierarchical modular organization. With respect to traditional methods in the community detection analysis, I develop a novel approach which allow us to find a common skeleton shared by the duplex structure-function network from which a new, optimal, brain partition can be extracted. Specifically, an algorithmic procedure rooted on the Expectation-Maximization Statistical technique (EM), has been developed to fit a generative network models on real brain data. In addition, a novel network index called Cross-Modularity, able to quantify the grade of similarity between two layers partitions, has been introducted. Finally using this quantity we make a comparison with classical single-layer community detection methods and then validate our approach.