To understand the vulnerability in having nodes in one network depend on nodes in another, consider the “smart grid,” an infrastructure system in which power stations are controlled by a telecommunications network that in turn requires power from the network of stations. In isolation, removing a few nodes from either network would do little harm, because signals could route around the outage and reach most of the remaining nodes. But in coupled networks, downed nodes in one automatically knock out dependent nodes in the other, which knock out other dependent nodes in the first, and so on. Scientists model this cascading process by calculating the size of the largest cluster of connected nodes in each network, where the answer depends on the size of the largest cluster in the other network. With the clusters interrelated in this way, a decrease in the size of one of them sets off a back-and-forth cascade of shrinking clusters.