It would be just a small exaggeration to say that we have reached the “network age.” A growing number of diverse systems are being represented as networks—collections of nodes that interact through links or connections. Think of engineered materials, intracellular media, organismal physiology, ecological systems, and swarming robots. Moreover, networks—be they financial, transportation, power-transmission, information-exchange, or social-interaction—are increasingly coming into existence as a result of human activity. (See the article by Adilson Motter and Réka Albert, Physics Today, April 2012, page 43.)
A defining characteristic of networks is their ability to propagate influence; they allow the state or behavior of one node to influence the state or behavior of others. Influence may spread across networks by way of ordinary contact processes such as epidemic spreading or diffusion. But influence may also spread through a fundamentally different process: a cascade.
Cascades are self-amplifying processes by which a relatively small...
