Synchronization and Non-Synchronization Properties of Directed Networks with Constant Out-Degree

Abstract Networks in which each node is connected to a fixed number of neighbors are raising more and more interest, both for modeling biological and social phenomena, and for improving the performance of distributed algorithms, like consensus problems, distributed sensing, motion coordination. In this paper we highlight some interesting properties about the spectrum of the eigenvalues of Laplacian matrices of networks with fixed number of neighbors, and connect them to the synchronization attitude of the network, through the Master Stability Function approach.