# Network Risk and Forecasting Power in Phase-Flipping Dynamical Networks

## Author Info

• B. Podobnik
• A. Majdandzic
• C. Curme
• Z. Qiao
• W. -X. Zhou
• H. E. Stanley
• B. Li
Registered author(s):

## 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.

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File URL: http://arxiv.org/pdf/1401.7450

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1401.7450.

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 Length: Date of creation: Jan 2014 Date of revision: Handle: RePEc:arx:papers:1401.7450 Contact details of provider: Web page: http://arxiv.org/

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