Title: Vulnerability and co-susceptibility determine the size of network cascades,
Abstract: 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.