The Optimal Setting for Multilayer Modularity Optimization in Multilayer Brain Networks*

Community detection plays a key role in the study of brain networks, as mechanisms of modular integration and segregation are known to characterize the brain functioning. Moreover, brain networks are intrinsically multilayer: they can vary across time, frequency, subjects, conditions, and meaning, according to different definitions of connectivity. Several algorithms for the multilayer community detection were defined to identify communities in time-varying networks. The most used one is based on the optimization of a multilayer formulation of the modularity, in which two parameters linked to the spatial (γ) and temporal (ω) resolution of the uncovered communities can be set. While the effect of different γ-values has been largely explored, which ω-values are most suitable to different purposes and conditions is still an open issue. In this work, we test the algorithm performances under different values of ω by means of ad hoc implemented benchmark graphs that cover a wide range of conditions. Results provide a guide to the choice of the ω-values according to the network features. Finally, we show an application of the algorithm to real functional brain networks estimated from electro-encephalographic (EEG) signals collected at rest with closed and open eyes. The application to real data agrees with the results of the simulation study and confirms the conclusion drawn from it.