k/2 intra-connections) with (1 − pin) × N × k/2 inter-connections, where pin designates the probability of intra-connections. The two nodes to be connected are chosen with a probability Πi = kiα/∑jkjα, where ki is the degree of node i, and α a parameter that tunes the preference of high-degree nodes. Finally, two of the subnetworks are connected through the top three highest-degree nodes. Comparison of r calculated from adjacency matrices generated with α = 0 (random selection) and α = 10 (rich-club selection) is summarized in Figure 4I. In hierarchically modular networks, the higher synchrony is achieved by coupling the sub-subnetworks through high-degree hub nodes. Together with the previous result (Figure 4H), the result underscores the importance of hubs in considering synchrony within NoNs.
