Figure 3

The role of coupling. (a) The half violin plot of \(P_{{\text{O}}}\) for real networks. The proportion \(P_\mathrm{E}\) of effective coupling and its trapezoidal numerical integration \(P_{\mathrm{I}}\) in (b) ER networks, (c) EX networks, and (d) SF networks as the function of the coupling density P, the average degree \(\langle k \rangle \) and the power exponent \(\gamma \), respectively. (e) The integration \(P_{\mathrm{I}}\) of real networks as the function of \(\langle k \rangle \). (f) The integration \(P_{\mathrm{I}}\) of real networks as the function of the correlation parameter \(\beta \). (g) The integration \(P_{\mathrm{I}}^\mathrm{rand-degree}\) obtained from the degree-preserving randomized version of the real networks, compared with \(P_{\mathrm{I}}^\mathrm{real}\).