Cluster dependency and synchronization of multilayer directed networks from a quotient graph perspective

This paper studies cluster dependence and synchronization in multilayer directed networks. Based on network quotient graphs, we provide a more efficient way to identify dependencies between clusters. By considering the relationships and interactions between clusters at a higher level of abstraction, this analysis can reduce the computational effort without requiring extensive computation on the original network. Furthermore, this paper investigates the impact of structural perturbations on network synchronization capabilities within a multilayer framework. Specifically, for the case where perturbations are applied to the dominant group, we study how changes in the network structure affect its cluster synchronization (CS) behavior. Finally, we employe a multilayer neural network model to validate the findings presented in this paper.