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A Cascading Failure Model of Directed Scale-Free Topology with Hierarchical Structure
Qian-Yue Wang, Ya-Qian Li, Yu-Jing Deng, He-Yao Zhao and Bin Liu

To study cascading failure of a directed hierarchical network, the difference between a directed network cascading failure process and an undirected network cascading failure process is analyzed. And the directed scale-free cascading failure model based on the hierarchical structure is proposed. Considering the node in-degree, neighbor-node in-degrees and node layers, the initial node load in the directed hierarchical network is defined and the proportional relation between the node capacity and initial load is established. Hierarchical heterogeneity is taken into account for load redistribution after node failure so that the additional load is allocated to the same or higher layer nodes. Then the relationship between network parameters and network robustness is obtained from the analyses of network cascading failure. Finally, the model is simulated using Matlab. Through the numerical and simulation analyses, the effectiveness of the proposed method in this paper is proved and this offers a foundation for further research on cascading failures of directed networks.

Keywords: Directed scale-free network; cascading failure; hierarchical structure; node load; node capacity; robustness.

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