Sharif Digital Repository

It has been shown that there is a relationship between the topological and spectral properties of a graph and its dynamics. However, most of the studies have not considered the direction of the links, even though most of the real networks are directed. In this thesis, we study the intrinsic relationship between the graphs’ structures, the spectral characteristics of their associated matrices, and the synchronization implications for different directed random graphs by changing their link directionality. To this end we make use of Kuramoto model for modeling the synchronization dynamics of the network. We show that, in contrast to the results of studies which suggest the λ2/λN as a measure of...