Abstract
A new node-importance ranking model and its solution algorithm for scale-free networks are proposed. The general idea is as follows: first, we construct a node-importance ranking model targeting the fastest network collapse, which is identified by the maximal variation in integrated network metrics. We then combine the genetic algorithm and variable neighbourhood search and improve it in initial population generation, neighbourhood search, and fitness evaluation. Finally, we investigate the BA network and container-shipping network. By comparison, the proposed method demonstrates a 7.9 and 16.8% improvement in effectiveness over betweenness and degree, respectively, in the BA network. The above indexes come to 15.1 and 41.3% in the container-shipping network. Moreover, the proposed algorithm reveals an 8.1 and 6.3% improvement in effectiveness, and a 63.7 and 67.1% reduction in computation time in the two cases, respectively. The research sheds new lights on not only analytical methods of complex theory but also practical application.
Similar content being viewed by others
Data availability
The data used to support the findings of this study are available from the corresponding author upon request.
References
Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512. https://doi.org/10.1126/science.286.5439.509
Callaway DS, Newman MEJ, Strogatz SH, Watts DJ (2011) Network robustness and fragility: percolation on random graphs. Phys Rev Lett 85(25):510–513. https://doi.org/10.1515/9781400841356.510
Aslan E, Çelik M (2019) Pre-positioning of relief items under road/facility vulnerability with concurrent restoration and relief transportation. IISE Trans 51:847–868. https://doi.org/10.1080/24725854.2018.1540900
Fasino D, Tonetto A, Tudisco F (2021) Generating large scale-free networks with the chung-lu random graph model. Networks 78:174–187. https://doi.org/10.1002/net.22012
Ma F, Wang X, Wang P, Luo X (2020) Dense networks with scale-free feature. Phys Rev E 101:052317. https://doi.org/10.1103/physreve.101.052317
Alves C, Ribeiro R, Sanchis R (2016) Large communities in a scale-free network. J Stat Phys 166:137–149. https://doi.org/10.1007/s10955-016-1676-8
Krasnytska M, Berche B, Holovatch Y, Kenna R (2021) Generalized Ising model on a scale-free network: An interplay of power laws. Entropy 23:1175. https://doi.org/10.3390/e23091175
Gao J, Barzel B, Barabási AL (2016) Universal resilience patterns in complex networks. Nature 530:307–312. https://doi.org/10.1038/nature16948
Zhang Y, Shao C, He S, Gao J (2020) Resilience centrality in complex networks. Phys Rev E 101:022304. https://doi.org/10.1103/physreve.101.022304
Fu G, Wilkinson S, Dawson RJ et al (2018) Integrated approach to assess the resilience of future electricity infrastructure networks to climate hazards. IEEE Syst J 12:3169–3180. https://doi.org/10.1109/jsyst.2017.2700791
O’Kelly ME (2014) Network Hub Structure and resilience. Netw Spat Econ 15(2):235–251. https://doi.org/10.1007/s11067-014-9267-1
Chattopadhyay S, Dai H, Young ED (2020) Maximization of robustness of interdependent networks under budget constraints. IEEE Trans Netw Sci Eng. 7(3):1441–1452. https://doi.org/10.1109/tnse.2019.2935068
Zhong J, Sanhedrai H, Zhang FM et al (2020) Network endurance against cascading overload failure. Reliab Eng Syst Saf 201:106916. https://doi.org/10.1016/j.ress.2020.106916
Xu Z, Julius AA, Chow JH (2018) Robust testing of cascading failure mitigations based on power dispatch and quick-start storage. IEEE Syst J 12:3063–3074. https://doi.org/10.1109/jsyst.2017.2686401
Fu X, Yang Y, Postolache O (2019) Invulnerability of clustering wireless sensor networks against cascading failures. IEEE Syst J 13:1431–1442. https://doi.org/10.1109/jsyst.2018.2849779
Hu S, Li G (2020) TMSE: a topology modification strategy to enhance the robustness of scale-free wireless sensor networks. Comput Commun 157:53–63. https://doi.org/10.1016/j.comcom.2020.04.007
Strisciuglio N, Lopez-Antequera M, Petkov N (2020) Enhanced robustness of convolutional networks with a push–pull inhibition layer. Neural Comput Appl 32:17957–17971. https://doi.org/10.1007/s00521-020-04751-8
Chiou SW (2020) A resilience-based signal control for a time-dependent road network with hazmat Transportation. Reliab Eng Syst Saf 193:106570. https://doi.org/10.1016/j.ress.2019.106570
Faramondi L, Oliva G, Panzieri S et al (2019) Network structural vulnerability: a multiobjective attacker perspective. IEEE Trans Sys Man Cybern-Syst 49:2036–2049. https://doi.org/10.1109/tsmc.2018.2790438
Shooshtarian L, Safaei F (2019) A maximally robustness embedding algorithm in virtual data centers with multi-attribute node ranking based on Topsis. J Supercomput 75:8059–8093. https://doi.org/10.1007/s11227-019-02981-9
Qiao T, Shan W, Yu G, Liu C (2018) A novel entropy-based centrality approach for identifying vital nodes in weighted networks. Entropy 20:261. https://doi.org/10.3390/e20040261
Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25:163–177. https://doi.org/10.1080/0022250x.2001.9990249
Jalili M (2011) Error and attack tolerance of small-worldness in complex networks. J Informetr 5:422–430. https://doi.org/10.1016/j.joi.2011.03.002
Bellingeri M, Cassi D, Vincenzi S (2014) Efficiency of attack strategies on complex model and real-world networks. Phys A 414:174–180. https://doi.org/10.1016/j.physa.2014.06.079
Fu CQ, Wang Y, Wang XY, Gao YJ (2018) Multi-node attack strategy of complex networks due to cascading breakdown. Chaos Solitons Fractals 106:61–66. https://doi.org/10.1016/j.chaos.2017.11.009
Schneider CM, Moreira AA, Andrade JS et al (2011) Mitigation of malicious attacks on networks. Proc Natl Acad Sci U S A 108:3838–3841. https://doi.org/10.1073/pnas.1009440108
Nie T, Guo Z, Zhao K, Lu ZM (2015) New attack strategies for complex networks. Phys A 424:248–253. https://doi.org/10.1016/j.physa.2015.01.004
Costa LD, Rodrigues FA, Travieso G, Villas Boas PR (2007) Characterization of complex networks: a survey of measurements. Adv Phys 56:167–242. https://doi.org/10.1080/00018730601170527
Wang N, Wu N, Dong LL et al (2016) A study of the temporal robustness of the growing global container-shipping network. Sci Rep 6:3421. https://doi.org/10.1038/srep34217
Yu A, Wang N, Wu N (2021) Scale-free networks: Characteristics of the time-variant robustness and vulnerability. IEEE Syst J 15:4082–4092. https://doi.org/10.1109/jsyst.2020.3022169
Schölkopf B, Smola A, Müller KR (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10:1299–1319. https://doi.org/10.1162/089976698300017467
Choi SW, Lee C, Lee JM et al (2005) Fault detection and identification of nonlinear processes based on kernel PCA. Chemom Intell Lab Syst 75:55–67. https://doi.org/10.1016/j.chemolab.2004.05.001
Cho JH, Lee JM, Sang WC et al (2005) Fault identification for process monitoring using kernel principal component analysis. Chem Eng Sci 60:279–288. https://doi.org/10.1016/j.ces.2004.08.007
Cochran JK, Horng SM, Fowler JW (2003) A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines. Comput Oper Res 30:1087–1102. https://doi.org/10.1016/s0305-0548(02)00059-x
Fan X, Hu S, He J (2017) A target recognition method for maritime surveillance radars based on hybrid ensemble selection. Int J Syst Sci 48:3334–3345. https://doi.org/10.1080/00207721.2017.1381283
Lai X, Hao JK, Fu ZH, Yue D (2021) Neighborhood decomposition-driven variable neighborhood search for capacitated clustering. Comput Oper Res 134:105362. https://doi.org/10.1016/j.cor.2021.105362
Friedrich C, Elbert R (2022) Adaptive Large neighborhood search for vehicle routing problems with transshipment facilities arising in City Logistics. Comput Oper Res 137:105491. https://doi.org/10.1016/j.cor.2021.105491
Luo Y, Pan Y, Li C, Tang H (2020) A hybrid algorithm combining genetic algorithm and variable neighborhood search for process sequencing optimization of large-size problem. Int J Comput Integr Manuf 33:962–981. https://doi.org/10.1080/0951192x.2020.1780318
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197. https://doi.org/10.1109/4235.996017
Deng Y, Wu J, Tan YJ (2016) Optimal attack strategy of complex networks based on Tabu Search. Phys A 442:74–81. https://doi.org/10.1016/j.physa.2015.08.043
Earnest DC, Yetiv S, Carmel SM (2012) Contagion in the transpacific shipping network: international networks and vulnerability interdependence. Int Interact 38:571–596. https://doi.org/10.1080/03050629.2012.726151
Ducruet C (2017) Multilayer dynamics of complex spatial networks: the case of global maritime flows (1977–2008). J Transp Geogr 60:47–58. https://doi.org/10.1016/j.jtrangeo.2017.02.007
Busan Port Authority (2017) Container statistics of Busan Port, Busan
China’s National Bureau of Statistics (2017) China Port Yearbook, China
Shooshtarian L, Safaei F (2020) A maximally robustness embedding algorithm in virtual data centers with multi-attribute node ranking based on Topsis. J Supercomput 75:8059–8093. https://doi.org/10.1007/s11227-019-02981-9
Bahutair M, Al Aghbari Z, Kamel I (2022) NodeRank: finding influential nodes in social networks based on interests. J Supercomput 78:2098–2124. https://doi.org/10.1007/s11227-021-03947-6
Funding
This work was supported by National Natural Science Foundation of China [Grant number: 72174034] and National Social Science Foundation of China [Grant number: 20&ZD070].
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yu, A., Wang, N. Node-importance ranking in scale-free networks: a network metric response model and its solution algorithm. J Supercomput 78, 17450–17469 (2022). https://doi.org/10.1007/s11227-022-04544-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11227-022-04544-x