Network Risk and Forecasting Power in Phase-Flipping Dynamical Networks

TL;DR

This paper models phase-flipping dynamics in scale-free networks with node and link failures, analyzing stochastic recovery effects, risk estimators, and hysteresis, with applications to economic and traffic networks.

Contribution

It introduces a stochastic model for phase-flipping in dynamical networks, deriving risk measures and analyzing hysteresis effects, which are novel in this context.

Findings

Probability of failure thresholds derived

Higher moments of active nodes/links calculated

Hysteresis observed in failure correlations

Abstract

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.