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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.
Highlights
Complex networks are increasingly being investigated in various fields of nature and society[1,2,3,4,5] and from different angles, such as collective behaviour[6,7,8,9,10], robustness[11,12], controllability[13,14], etc
Concerning the dependency property, Parshani et al.[18] proposed an analytical model to study the robustness of networks that include both connectivity and dependency links and found, surprisingly, that a broader degree distribution increases the vulnerability of these networks to random failures, which is opposite to how networks containing only connectivity links behave
In the section of results, firstly, we present an evolving network model consisting of failure mechanisms, a recovery mechanism and a dynamic mechanism of dependency groups
Summary
Complex networks are increasingly being investigated in various fields of nature and society[1,2,3,4,5] and from different angles, such as collective behaviour[6,7,8,9,10], robustness[11,12], controllability[13,14], etc. The dependency property, modelled by dependency links[18,19,20], has been proposed to study the effects of dependency among nodes on the evolution of complex networks, especially for cascading failures. Networks with dependency groups or links have been studied in the form of interdependent networks and multilayer networks, showing the fragility of networks when nodes depend on each other[20,24] Among these efforts, some new phenomena have been found, e.g., assortativity[25] and coupling strength[26] decrease the robustness of interdependent networks, intersimilarity[27] and short dependency distances[28] have considerable effects on reducing the cascading failures, and percolation transitions are not always sharpened by making networks interdependent[29]. It is necessary to explore cascading failures of networks under dynamical dependency
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