A Novel Approach for Optimizing Synchronizability in Multilayer Complex Networks via Association Schemes

Optimizing synchronizability in multilayer complex networks is a challenging problem due to the absence of a unique set of weights on the Pareto frontier. Addressing this problem, a novel model for multilayer networks has been proposed that leverages the underlying graphs derived from edge-transitive association schemes. Then, based on the stability interval originating from the master stability function (MSF) approach for the Rössler system, an optimal point with the most negative MSF value is selected as the most stable point on the Pareto Frontier. Two distinct solution methods for optimizing the synchronizability measure, based on linear programming (LP) and the direct solution, have been provided. The effectiveness of these methods is demonstrated on cycle and hypercube multilayer networks through both analytical results and simulations.