By interpreting a temporal network as a trajectory of a latent graph
dynamical system, here we introduce the concept of dynamical instabil-
ity of a temporal network, and accordingly derive a measure to estimate
the network Maximum Lyapunov Exponent (nMLE) of a temporal net-
work trajectory. By building and extending classical algorithmic methods
from nonlinear time series analysis into the network realm, we show
how to quantify sensitive dependence on initial conditions and practi-
cally estimate the nMLE directly from single network trajectories. We
validate our method for a range of synthetic generative network models
and discuss its applicability in formulating and answering new questions
on the chaotic nature of interacting systems in different disciplines.
