The dependency among nodes has significant effects on the cascading failures of complex networks. Although the prevention of cascading failures on multilayered networks in which the failures of nodes in one layer affect the functioning of nodes in other layers has been widely investigated, the prevention of catastrophic cascade has rarely been addressed to single-layer networks where nodes are grouped and nodes within the same group are dependent on each other. For such networks, we find that it is already enough to prevent abrupt catastrophic collapses by randomly reinforcing a constant density of nodes. More importantly, we give the analytical solutions to the proportion of needed reinforced nodes for three typical networks, i.e., dependent Erdős-Rényi (ER), random regular (RR), and scale-free (SF) networks. Interestingly, the density of reinforced nodes is a constant 0.1756, which holds true for ER networks with group size 2 regardless of average degree, RR, and SF networks with a large average degree. Also, we find the elegant expression of the density with any group size. In addition, we find a hybrid phase transition behavior, which is present in RR and SF networks while absent in ER networks. Our findings might shed some new light on designing more resilient infrastructure networks.
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Eradicating abrupt collapse on single network with dependency groups
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August 2019
Research Article|
August 12 2019
Eradicating abrupt collapse on single network with dependency groups
Special Collection:
Focus Issue: Complex Network Approaches to Cyber-Physical Systems
Jiarong Xie;
Jiarong Xie
School of Data and Computer Science, Sun Yat-sen University
, Guangzhou 510006, China
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Youyou Yuan;
Youyou Yuan
School of Data and Computer Science, Sun Yat-sen University
, Guangzhou 510006, China
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Zhengping Fan;
Zhengping Fan
School of Data and Computer Science, Sun Yat-sen University
, Guangzhou 510006, China
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Jiahai Wang;
Jiahai Wang
School of Data and Computer Science, Sun Yat-sen University
, Guangzhou 510006, China
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Jiajing Wu
;
Jiajing Wu
School of Data and Computer Science, Sun Yat-sen University
, Guangzhou 510006, China
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Yanqing Hu
Yanqing Hu
a)
School of Data and Computer Science, Sun Yat-sen University
, Guangzhou 510006, China
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a)
Electronic mail: huyanq@mail.sysu.edu.cn
Note: The paper is part of the Focus Issue, “Complex Network Approaches to Cyber-Physical Systems.”
Chaos 29, 083111 (2019)
Article history
Received:
February 17 2019
Accepted:
July 16 2019
Citation
Jiarong Xie, Youyou Yuan, Zhengping Fan, Jiahai Wang, Jiajing Wu, Yanqing Hu; Eradicating abrupt collapse on single network with dependency groups. Chaos 1 August 2019; 29 (8): 083111. https://doi.org/10.1063/1.5093077
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