Optimal Synchronizability in Networks of Coupled Systems: Topological View

Many engineered and natural systems are modeled as networks of coupled systems. Synchronization is one of their crucial and well-studied behaviors. Uniform coupling strength has been the benchmark practice in the majority of the literature. This paper considers nonuniform coupling strength, and a modified approach to the problem of synchronizability optimization, enabling a reduction to a spectral radius minimization problem, which can reach a unique optimal point on the Pareto Frontier. It is established that adding any edge to a connected graph can only improve synchronizability in this optimal measure. This result is utilized for developing a hierarchy between topologies. It is shown that several proposed structural parameters, including betweenness centrality, do not have any simple relationship to the optimal synchronizability measure.