Dynamical and spectral properties of complex networks

Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of networks and different dynamics. We show that the main dependence of the synchronization time is on the smallest nonzero eigenvalue of the Laplacian matrix, in contrast to other proposals in terms of the spectrum of the adjacency matrix. Then, this topological property becomes the most relevant for the dynamics.