Dynamics and Directionality in Complex Networks

We investigate how we can improve the synchronizability of complex networks simply by changing the link direction while conserving the local link weights and topology. Performing the linear stability analysis of synchronization and numerical simulation of the Kuramoto model in the directed networks, we find that while a random assignment of link directions generally weakens the degree of synchronization, a properly organized directionality can systematically enhance the network synchronization. In this respect, we suggest a simple method of changing the link direction according to the larger residual degree starting from small residual degree nodes. This result provides plausible applications to control the synchronizability of systems in various fields.