Modular synchronization in complex networks with a gauge Kuramoto model

¹  Bioanalysis and Biotransformation Research Center, Korea Institute of Science and Technology Seoul 136-791, Korea
²  Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University Seoul 151-747, Korea

Corresponding author: bkahng@snu.ac.kr

Received: 12 June 2008
Accepted: 6 August 2008

Abstract

We modify the Kuramoto model for synchronization on complex networks by introducing a gauge term that depends on the edge betweenness centrality (BC). The gauge term introduces additional phase difference between two vertices from 0 to as the BC on the edge between them increases from the minimum to the maximum in the network. When the network has a modular structure, the model generates the phase synchronization within each module, however, not over the entire system. Based on this feature, we can distinguish modules in complex networks, with relatively little computational time of , where N and L are the number of vertices and edges in the system, respectively. We also examine the synchronization of the modified Kuramoto model and compare it with that of the original Kuramoto model in several complex networks.