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