title: Robustness and Vulnerability of Networks with Dynamical Dependency Groups.
abstract: The dependency property and self-recovery of failure nodes both have great effects on the robustness of networks during the cascading process. Existing investigations focused mainly on the failure mechanism of static dependency groups without considering the time-dependency of interdependent nodes and the recovery mechanism in reality. In this study, we present an evolving network model consisting of failure mechanisms and a recovery mechanism to explore network robustness, where the dependency relations among nodes vary over time. Based on generating function techniques, we provide an analytical framework for random networks with arbitrary degree distribution. In particular, we theoretically find that an abrupt percolation transition exists corresponding to the dynamical dependency groups for a wide range of topologies after initial random removal. Moreover, when the abrupt transition point is above the failure threshold of dependency groups, the evolving network with the larger dependency groups is more vulnerable; when below it, the larger dependency groups make the network more robust. Numerical simulations employing the Erdős-Rényi network and Barabási-Albert scale free network are performed to validate our theoretical results.
authors.affiliation: School of Reliability and Systems Engineering, Beihang University, Beijing, 100191, P.R. China.
authors.forename: Ya-Nan
authors.initials: YN
authors.lastname: Bai
authors.affiliation: School of Reliability and Systems Engineering, Beihang University, Beijing, 100191, P.R. China.|Key Laboratory of Science &Technology on Reliability &Environmental Engineering, Beihang University, Beijing, 100191, P.R. China.
authors.forename: Ning
authors.initials: N
authors.lastname: Huang
authors.affiliation: School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, P.R. China.
authors.forename: Lei
authors.initials: L
authors.lastname: Wang
authors.affiliation: Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu, 730000, P.R. China.
authors.forename: Zhi-Xi
authors.initials: ZX
authors.lastname: Wu