Figure 1

Schematic of the rules of functionality of the model. Black links represent internal connections and orange links the supplies between networks. The state of the nodes varies according to their color: functional nodes (), nodes that do not fulfill the internal rule of functionality () and nodes that fail due to the initial damage (). In addition, we have nodes that externally fail because they do not get enough supply from the other network ();. In panel (a) we show the three internal rules of functionality for a node i (marked with the blue arrow) to be functional: (I) it must be connected to the GC (represented by the ∞ symbol), (II) it must belong to a component of size h which survives with probability 1 − q(h) (in this case k ^* ≡ k _i ^*), or (III) it must have a number of neighbors equal to or greater than k ^* ≡ k _i ^* (we show k ^* = 2). In panel (b) we show the external rule of functionality for k _s ^* = 1, and k _s ^* = 2 in panel (c). In these cases P _sA (k) = P _sB (k) = δ _k,3, however, not all supplies are shown, nor are the internal connectivity links.