Fig. 5

Comparison between the first-order perturbative expansion and the real behavior of the network, for the topologies \(C_{10}\), \(K_{10}\), \(\mathcal {BC}_{3,10} (4,5,5 )\) and \(Q_{4}\). The parameters used for the simulation are \(\sigma=0.1\) and those shown in Table 1 and by Eq. (7.1). Correlation has been calculated by simulating equations in (2.1) \(10\mbox{,}000\) times with the Euler–Maruyama scheme and then by applying a Monte Carlo method. Finally, this result is compared to the first-order analytical formula of the correlation. The figure shows good agreement, which validates the use of the perturbative approach