Finding an hidden common partition in duplex structure-function brain networks

We investigate the intricate relationship between human brain structure and function from a complex networks perspective. Indeed, several works in neuroimaging data analysis indicate the presence of robust partitions in both structural and functional networks, thus confirming that these two networks are interdependent. 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 relation, we focus on groups of nodes making a comparison among structural and functional neural networks by exploiting their hierarchical modular organization. With respect to traditional methods in the community detection framework, we have developed a novel approach which allow us to figure out a common skeleton shared by structure and function in brain network. Using this, a new, and optimal common partition, can be extracted from duplex structure-function networks. Specifically, an algorithm, based on a probabilistic network model, has been developed to design an unsupervised multi-layer community detection. Hence, a numerical implementation has been rooted on the Expectation-Maximization technique (EM) to perform statistical inference on real brain data. We tested our algorithm on structural connectivity (SC) and resting state functional connectivity networks (rsFC) extracted from 12 healthy patients. Furthermore, we define a novel network measure called Cross-Modularity X, suitable to quantify the grade of similarity between two layers partitions. Finally, in order to validate our clustering algorithm, we use this quantity to make a comparison with classical single-layer community detection methods. As main result we obtain that the correlations between structural and functional networks are improved when the comparison has been made at the level of our extracted partition