Networks' modulation: How different structural network properties affect the global synchronization of coupled Kuramoto oscillators

In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity properties among these objects drives the global dynamics in a complex fashion and affects the global degree of synchrony of the system. Here we study the impact of such types of different network architectures, such as Fully-Connected, Random, Regular ring lattice graph, Small-World and Scale-Free in the global dynamical activity of a system of coupled Kuramoto phase oscillators. We fix the external stimulation parameters and we measure the global degree of synchrony when different fractions of nodes receive stimulus. These nodes are chosen either randomly or based on their respective strong/weak connectivity properties (centrality, shortest path length and clustering coefficient). Our main finding is, that in Scale-Free and Random networks a sophisticated choice of nodes based on their eigenvector centrality and average shortest path length exhibits a systematic trend in achieving higher degree of synchrony. However, this trend does not occur when using the clustering coefficient as a criterion. For the other types of graphs considered, the choice of the stimulated nodes (randomly vs selectively using the aforementioned criteria) does not seem to have a noticeable effect.