On opinion formation and synchronization in multiplex networks

Abstract

We study the process of synchronization that takes place on multiplex networks, i.e., on a set of networks linked through interconnected layers. As a measure for synchronization we use the eigenratio between the largest and the smallest eigenvalue of the Laplacian matrix of the multiplex graph. Using this measure we analyze how the synchronization depends on the weight of the interconnection links in a given multiplex network. Furthermore, the main results of this work show that even though a network has a bigger eigenratio than other networks, when it is multiplexed with other networks its synchronization rate can be slowed. The results from this work can be easily applied in modeling and analyzing the process of opinion formation in social networks and synchronization in Smart Grid.