Optimizing synchronizability of small-world networks via adjusting edge weights

Abstract This article explores the optimization of synchronizability in small-world networks via adjusting edge weights and evaluates the performance of four edge selection strategies: Edge Perturbation, Edge Betweenness Centrality, Degree Assortativity Coefficient, and Random Change. We examine two types of synchronous regions: unbounded and bounded. In the unbounded synchronous region, synchronizability exhibits a positive correlation with edge weight modifications. While for the bounded synchronous region, synchronizability depends on the edge selection strategy and has no definite relationship with edge weight adjustments. Among these four strategies, Edge Betweenness Centrality proves effective in enhancing synchronizability in the unbounded region, while Edge Perturbation shows superior performance across small-world networks with varying parameter settings for the bounded region. To validate the effectiveness of our methods, we apply them to real-world networks, demonstrating their practical relevance.