  In order to model volatile real-world network behavior, we analyze
phase-flipping dynamical scale-free network in which nodes and links fail and
recover. We investigate how stochasticity in a parameter governing the recovery
process affects phase-flipping dynamics, and find the probability that no more
than q% of nodes and links fail. We derive higher moments of the fractions of
active nodes and active links, $f_n(t)$ and $f_{\ell}(t)$, and define two
estimators to quantify the level of risk in a network. We find hysteresis in
the correlations of $f_n(t)$ due to failures at the node level, and derive
conditional probabilities for phase-flipping in networks. We apply our model to
economic and traffic networks.
