  A central issue in the study of large complex network systems, such as power
grids, financial networks, and ecological systems, is to understand their
response to dynamical perturbations. Recent studies recognize that many real
networks show nonnormality and that nonnormality can give rise to
reactivity--the capacity of a linearly stable system to amplify its response to
perturbations, oftentimes exciting nonlinear instabilities. Here, we identify
network structural properties underlying the pervasiveness of nonnormality and
reactivity in real directed networks, which we establish using the most
extensive data set of such networks studied in this context to date. The
identified properties are imbalances between incoming and outgoing network
links and paths at each node. Based on this characterization, we develop a
theory that quantitatively predicts nonnormality and reactivity and explains
the observed pervasiveness. We suggest that these results can be used to
design, upgrade, control, and manage networks to avoid or promote network
instabilities.
