|
|
|
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.
|
Received: 02 September 2020
Revised: 04 December 2020
Accepted manuscript online: 17 December 2020
|
|
PACS:
|
05.10.-a
|
(Computational methods in statistical physics and nonlinear dynamics)
|
| |
64.60.aq
|
(Networks)
|
| |
89.75.-k
|
(Complex systems)
|
| |
89.75.Hc
|
(Networks and genealogical trees)
|
|
| 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
|
[1] Jeong H, Tombor B, Albert R, Oltvai Z N and Barabasi A L 2000 Nature 407 651
[2] Cohen R, Erez K, Benavraham D and Havlin S 2000 Phys. Rev. Lett. 85 4626
[3] Ebel H, Mielsch L and Bornholdt S 2002 Phys. Rev. E 66 035103
[4] Goh K, Oh E, Kahng B and Kim D 2003 Phys. Rev. E 67 017101
[5] Gross T, Dlima C J D and Blasius B 2006 Phys. Rev. Lett. 96 208701
[6] Wang J and Rong L 2009 Safety Sci. 47 1332
[7] Zhu Y, Yan J, Sun Y and He H 2014 IEEE Trans. Parallel and Distributed Syst. 25 3274
[8] Zhang Z G, Ding Z, Fan J F, Meng J, Ding Y M, Ye F F and Chen X S 2015 Chin. Phys. B 24 090201
[9] Cai Y, Cao Y, Li Y, Huang T and Zhou B 2016 IEEE Trans. Smart Grid 7 530
[10] Hu F, Yeung C H, Yang S, Wang W and Zeng A 2016 Sci. Rep. 6 24522
[11] Cohen R, Erez K, Benavraham D and Havlin S 2001 Phys. Rev. Lett. 86 3682
[12] Cohen R, Havlin S and Benavraham D 2003 Phys. Rev. Lett. 91 247901
[13] Beygelzimer A, Grinstein G, Linsker R and Rish I 2005 Physica A 357 593
[14] Schneider C M, Moreira A A, Andrade Jr J S, Havlin S and Herrmann H J 2011 Proc. Natl. Acad. Sci. USA 108 3838
[15] Pocock M J O, Evans D M and Memmott J 2012 Science 335 973
[16] Dong G, Gao J, Du R, Tian L, Stanley H E and Havlin S 2013 Phys. Rev. E 87 052804
[17] Min B, Yi S D, Lee K M and Goh K I 2014 Phys. Rev. E 89 042811
[18] Callaway D S, Newman M E J, Strogatz S H and Watts D J 2000 Phys. Rev. Lett. 85 5468
[19] Albert R, Jeong H and Barabasi A L 2000 Nature 406 378
[20] Holme P, Kim B J, Yoon C N and Han S K 2002 Phys. Rev. E 65 056109
[21] Iyer S, Killingback T, Sundaram B and Wang Z 2013 PLoS ONE 8 e59613
[22] Zhang Z Z, Xu W J, Zeng S Y and Lin J R 2014 Chin. Phys. B 23 088902
[23] Buldyrev S V, Parshani R, Paul G, Stanley H E and Havlin S 2010 Nature 464 1025
[24] Gao J, Buldyrev S V, Havlin S and Stanley H E 2011 Phys. Rev. Lett. 107 195701
[25] Motter A E and Lai Y 2002 Phys. Rev. E 66 065102
[26] Wang B and Kim B J 2007 Europhys. Lett. 78 48001
[27] Li P, Wang B H, Sun H, Gao P and Zhou T 2008 Eur. Phys. J. B 62 101
[28] Wu Z, Peng G, Wang W, Chan S and Wong E 2008 J. Stat. Mech.: Theory and Experiment 2008 05013
[29] Wang W and Chen G 2008 Phys. Rev. E 77 026101
[30] Mirzasoleiman B, Babaei M, Jalili M and Safari M 2011 Phys. Rev. E 84 046114
[31] Wang J 2013 Safety Sci. 53 219
[32] Lv C C, Si S B, Duan D L and Zhan R 2017 Physica A 471 837
[33] Majdandzic A, Podobnik B, Buldyrev S V, Kenett D Y, Havlin S and Stanley H E 2014 Nat. Phys. 10 34
[34] Shang Y L 2016 Sci. Rep. 6 30521
[35] Gallos L K and Fefferman N H 2015 Phys. Rev. E 92 052806
[36] Shang Y L 2015 Phys. Rev. E 91 042804
[37] Shang Y L 2016 J. Stat. Mech.: Theory and Experiment 2016 1742
[38] Duan D, Ling X, Wu X, Ouyang D and Zhong B 2014 Physica A 416 252
[39] Barabasi A L and Albert R 1999 Science 286 509 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
