Next, we examine the effect of the network topology on the synchrony of a single network. We consider four types of topologies: random, SW, SF, and super-hub (Figure 2A). In all four networks, a synchronized state, which we define as r > 0.9, is achieved when K is sufficiently high. Figure 2B shows the dependence of r on K for networks with different topologies. Comparison of the random, SF, and super-hub networks reveals that random networks synchronize at the lowest K (Figure 2B). When the nodes are inhomogeneous, the variation in the natural frequencies of the hub nodes degrades the synchronization in the SF and super-hub networks. This trend is confirmed analytically from the evaluation of r from the synchrony alignment function (Figure 2C).
