The mechanism of Network (ii) being more synchronizable than Network (iii) can be understood from the previous discussion regarding the steady-state frequency of the coupled subnetworks (Figure 5A). Considering that two coupled subnetworks synchronize at their mean frequency, Network (ii) can be coarse-grained into a set of interacting subnetwork-pairs with the average natural frequency of 4.5-Δω2 (constituted by the interaction of Subnetworks 1 and 2) and 4.5 (Subnetworks 1 and 3). For Network (iii), the frequencies are 4.5-Δω2 (Subnetworks 1 and 2) and 4.5+Δω2 (Subnetworks 2 and 3). The delta in these frequencies is smaller for Network (ii) than for Network (iii); hence, Network (ii) can withstand a larger deviation in the natural frequencies. However, the shift in the r-Δω relationship with the connection strategy is nonlinear, and the value of Δω for realizing a certain r in Network (ii) is not equal to 2 × Δω for Network (iii).
