Vulnerability and co-susceptibility determine the size of network cascades

In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail, in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Here, we develop a statistical framework that can predict cascade size distributions by incorporating two ingredients only: the vulnerability of individual components and the co-susceptibility of groups of components (i.e., their tendency to fail together). Using cascades in power grids as a representative example, we show that correlations between component failures define structured and often surprisingly large groups of co-susceptible components. Aside from their implications for blackout studies, these results provide insights and a new modeling framework for understanding cascades in financial systems, food webs, and complex networks in general.