Alternating synchronizability of complex clustered networks with regular local structure

Small network distance and homogeneous degree distribution have been found to be critical to efficient network synchronization. In this paper, we investigate the synchronizability of clustered networks with regular subnetworks and report a counterintuitive phenomenon: As the density of intracluster links is increased, the network exhibits strong and weak synchronizability in an alternating manner. A theory based on analyzing the eigenvalues and eigenvectors of the coupling matrix is provided to explain this phenomenon. The relevance of the network model to tissue organization for intercellular communication in biological systems is discussed. An implication is that, in order to achieve synchronization, local coupling density in the network needs to be tuned properly.