Figure 9. Mean-field results for increasing loads The fraction of failures f grows as a function of the initial load per link until the first order transition.

For our mean-field model no islanding is possible since the fraction of failed nodes after the transition is f = 1 (all the links have failed). Left panel: For an initial distribution p(C) ∝ const, the approach to the first order jump is smoother. Right panel: For an initial distribution p(C) ∝ C⁻² (typical of larger networks), the first order jump happens with no apparent precursors.