title: Structural properties of the synchronized cluster on complex networks.
abstract: We investigate how the largest synchronized connected component (LSCC) is formed and evolves to achieve a global synchronization on complex networks using Kuramoto model. In this study we use two different networks, Erdösi-Rényi network and Barabási-Albert network. From the finite-size scaling analysis, we find that the scaling exponents for the percolation order parameter and mean cluster size on both networks agree with the mean-field percolation theory, beta=gamma=1. We also find that the finite-size scaling exponent, nu, also agrees with the mean-field percolation result, nu=3. Moreover, we also show that the cluster size distributions are identical with the mean-field percolation distribution on both networks. Combining with the analysis for the merging clusters, we directly show that the LSCC on both networks evolves by merging clusters of various sizes.
authors.affiliation: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea. ykim@khu.ac.kr
authors.forename: Yup
authors.initials: Y
authors.lastname: Kim
authors.forename: Yongjin
authors.initials: Y
authors.lastname: Ko
authors.forename: Soon-Hyung
authors.initials: SH
authors.lastname: Yook