as indicated by the black line.

Next, we consider the cases with disorder, plotted in Fig. \[fig:PhaseDiagram\] (b) and (c), and we observe the appearance of the intermediate regimes QB and D1. These two regimes appear around the BDT and upon increasing disorder $\delta \lambda$ progressively span the entire diagram, which is a clear indication that disorder controls the position of these transitions. In addition, the transitions between the regimes are less sharp when the disorder is larger, as testified by the less homogeneously colored pie-chart symbols. Indeed, the mechanical responses of networks with large $\delta \lambda$ depend on the exact realization of the network (exact distribution of threshold values and their spatial organization), even when having the same $\mu_M/\mu_S$ and $\left<\lambda_S\right>$, especially around boundaries between different regimes. A similar dependence of the location of the B-to-QB and D1-to-D2 transitions on disorder is also predicted by the MS model (dashed lines, see Supplemental Material for further information [@supp]). At low disorder, the location of the boundaries corresponds well between the models, but at high disorder the boundaries move away from each other. This comparison reveals that network structure is not essential for the occurrence of any of the four regimes, 