Synchronization-based scalability of complex clustered networks

Complex clustered networks arise in biological, social, physical, and technological systems, and the synchronous dynamics on such networks have attracted recent interests. Here we investigate system-size dependence of the synchronizability of these networks. Theoretical analysis and numerical computations reveal that, for a typical clustered network, as its size is increased, the synchronizability can be maintained or even enhanced but at the expense of deterioration of the clustered characteristics in the topology that distinguish this type of networks from other types of complex networks. An implication is that, for a large network in a realistic situation, if synchronization is important for its function, then most likely it will not have a clustered topology.