Altering synchronizability by adding and deleting edges for scale-free networks

In this paper we propose two methods for altering the synchronizability of scale-free networks: (1) adding edges between the max-degree nodes and min-degree nodes; (2) deleting edges between the max-degree nodes and max-degree nodes. After adding and deleting edges, we find that the former, adding process can weaken synchronizability, while the latter, deleting process can enhance it; the two processes (adding and deleting) can preserve the scale-free structure; the study of the average clustering coefficient indicates that it is not the most closely correlated with the synchronizability among the topological features considered. Our work also suggests that there are some essential relations between the network synchronization and the dynamics of economic systems. They can be used to deal with some problems in the real world, such as relieving the economic crisis. In addition, the adding and deleting processes may have potential applications in modifying network structure, in view of their low cost.