Influence of Local Change of the Network Topology on a Synchronization Phenomenon

Abstract

There are many studies about the influence of network structure on phenomena taking place on the network. Most of such the studies focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though local structure has a significant effect on the dynamics of some phenomena. In addition, there is little research that directly addresses the local operations which can easily change the local structure even when it is difficult to modify the global statistics. In this paper, we study a relationship between the convergence time in the consensus problem which induced from a synchronization process in a complex network and the change of local network structure. The local structure is changed by means of exchange of two edges with maintaining the degree distribution. First, we introduce the product of two betweenness centralities calculated at both ends of an edge as a new index which represents the change in local structure. Several relationships between the index and the convergence time are found. And then, we show the possibility that the network in which the convergence time is controllable can be generated.