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Recently, some coarse-graining methods based on network synchronization have been proposed to reduce the network size while preserving the synchronizability of the original network. In this paper, we investigate the effects of the coarse graining process on synchronizability over complex networks under different average path lengths and different degrees of distribution. A large amount of experiments demonstrate a close correlation between the average path length, the heterogeneity of the degree distribution and the ability of spectral coarse-grained scheme in preserving the network synchronizability. We find that synchronizability can be well preserved in spectral coarse-grained networks when the considered networks have a longer average path length or a larger degree of variance.

Influence of Topological Properties of Complex Networks on the Effect of Spectral Coarse-Grained Network