Increasing synchronizability in a scale-free network via edge elimination

In this paper, synchronization of a Scale-Free (SF) network of chaotic oscillators is addressed. Synchronizability is increased, while eliminating edges in a SF network. We propose two novel methods using perturbation theory as an edge selection criteria, to eliminate the least amount of edges. Also we modified one existing method from the literature. These methods yielded the best results at increasing synchronizability the most per edge eliminated, while avoiding node isolation. These three strategies were tested in SF networks with different average degrees, and compared with other five strategies found in literature. Some five criterions on the selection of the method are given. This paper is especially interested in Case 3 of the Master Stability Function, which allows synchronizability to be defined. Therefore we use chaotic Rössler oscillators as nodes in the SF networks.