Spectral coarse graining of complex clustered networks

• We investigate the effects of the coarse graining process on synchronizability over complex clustered networks.
• There is a close correlation between the degree of clustering of the initial network and the ability of spectral coarse graining in preserving the network synchronizability.
• Synchronizability can be well preserved if the considered network has a clear cluster structure, whereas this is not so for networks with vague clustering.

Synchronization in complex dynamical networks is in the focus of network science today, where intensive efforts have been devoted to understanding its mechanisms and developing basic theories with applications. However, the sheer sizes of large-scale networks have been the main hurdle in such analysis and applications. Recently, a coarse graining scheme based on network synchronization was proposed to reduce the network size while preserving the synchronizability of the original network. In this research, we investigate the effects of the coarse graining process on synchronizability over complex clustered networks. Numerous experiments demonstrate a close correlation between the degree of clustering of the initial network and the ability of spectral coarse graining in preserving the network synchronizability. It is found that synchronizability can be well preserved after applying the spectral coarse graining if the considered network has a clear cluster structure, whereas this is not so for networks with vague clustering. Since most real-world networks have prominent cluster structures, this research provides new insights into understanding large-scale dynamical networks and analyzing their complex topological characteristics as well as synchronization mechanisms.