Network Risk and Forecasting Power in Phase-Flipping Dynamical Networks
  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. 
B. Podobnik, A. Majdandzic, C. Curme, Z. Qiao, W.-X. Zhou, H. E.   Stanley, and B. Li
physics.soc-ph physics.data-an q-fin.GN