Structural properties of the synchronized cluster on complex networks

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, β=γ=1. We also find that the finite-size scaling exponent, ν̄, also agrees with the mean-field percolation result, ν̄ =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.