Dynamical robustness of networks based on betweenness against multi-node attack

Zi-Wei Yuan(袁紫薇)^{1,2}, Chang-Chun Lv(吕长春)^{1,2}, Shu-Bin Si(司书宾)^{1,2,†}, and Dong-Li Duan(段东立)^{3}

1 School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China; 2 Key Laboratory of Industrial Engineering and Intelligent Manufacturing(Ministry of Industry and Information Technology), Xi'an 710072, China; 3 School of Information and Control Engineering, Xi'an University of Architecture and Technology, Xi'an 710311, China

Abstract We explore the robustness of a network against failures of vertices or edges where a fraction $f$ of vertices is removed and an overload model based on betweenness is constructed. It is assumed that the load and capacity of vertex $i$ are correlated with its betweenness centrality $B_i$ as $B_i^\theta$ and $(1+\alpha) B_i^\theta$ ($\theta$ is the strength parameter, $\alpha$ is the tolerance parameter). We model the cascading failures following a local load preferential sharing rule. It is found that there exists a minimal $\alpha_{\rm c}$ when $\theta$ is between 0 and 1, and its theoretical analysis is given. The minimal $\alpha_{\rm c}$ characterizes the strongest robustness of a network against cascading failures triggered by removing a random fraction $f$ of vertices. It is realized that the minimal $\alpha_{\rm c}$ increases with the increase of the removal fraction $f$ or the decrease of average degree. In addition, we compare the robustness of networks whose overload models are characterized by degree and betweenness, and find that the networks based on betweenness have stronger robustness against the random removal of a fraction $f$ of vertices.

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 71771186, 71631001, and 72071153) and the Natural Science Foundation of Shaanxi Province, China (Grant Nos. 2020JM-486 and 2020JM-486).

Corresponding Authors:
Shu-Bin Si
E-mail: sisb@nwpu.edu.cn

Cite this article:

Zi-Wei Yuan(袁紫薇), Chang-Chun Lv(吕长春), Shu-Bin Si(司书宾), and Dong-Li Duan(段东立) Dynamical robustness of networks based on betweenness against multi-node attack 2021 Chin. Phys. B 30 050501

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