FIG. 1.

Illustration of the threshold assignment for central failures. The interval $\left]F\right(k-1),F(k\left)\right]$ (in cyan color) represents (the fraction of) all nodes with degree $k$ in the network, while the blue interval corresponds to nodes with threshold $\theta \le x$. Their intersection, the purple interval, can thus be associated with all nodes in the network which have degree $k$ and a threshold smaller than or equal to $x$.