Abstract:This paper proposes a high-low-order coupled network model to gain a deeper understanding of the interdependent relationships in real-world network systems and address the cascade failure issues faced by complex networks and their higher-order networks. This model describes the interdependencies between complex networks (lower-order networks) and their higher-order organizations (higher-order networks). Their vulnerability is analyzed by subjecting the high-low-order coupled networks to random attacks. The study reveals that high-low-order coupled networks exhibit greater vulnerability to random attacks than standalone lower-order networks. This finding underscores the importance of considering the interdependencies between high and low-order networks in designing and managing complex network systems, particularly in preventing cascade failures, where special attention should be paid to the vulnerabilities of these interdependent structures.
张成军, 姚辉, 雷毅, 夏登辉, 李琪, 沈鑫禹, 钱铭, 余文斌. 高低阶耦合网络的鲁棒性研究[J]. 复杂系统与复杂性科学, 2024, 21(3): 17-22.
ZHANG Chengjun, YAO Hui, LEI Yi, XIA Denghui, LI Qi, SHEN Xinyu, QIAN Ming, YU Wenbin. Study on the Robustness of High-low-order Coupling Networks[J]. Complex Systems and Complexity Science, 2024, 21(3): 17-22.
[1] NICOL D M, YAN G. High-performance simulation of low-resolution network flows[J]. Simulation, 2006, 82(1): 21-42. [2] WERNER N E, BUMPUS M F, ROCK D. Involvement in internet aggression during early adolescence[J]. J Youth Adolesc, 2010, 39(6): 607-619. [3] BABA T, MATSUDA S. Tracing network attacks to their sources[J]. IEEE Internet Computing, 2002, 6(2): 20-26. [4] ERDÖS P, RÉNYI A. On random graphs[J]. Publicationes Mathematicae Debrecen, 1959, 6: 290-297. [5] ERDÖS P, RÉNYI A. On the evolution of random graphs[J]. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 1960, 5(1): 17-60. [6] PRICE D. Networks of scientific papers[J]. Science, 1965, 149(3683): 510-515. [7] PRICE D. A general theory of bibliometric and other cumulative advantage processes[J]. Journal of the American Society for Information Science, 1976, 27(5): 292-306. [8] WATTS D J, STROGATZ S H. Collective dynamics of "small-world" networks[J]. Nature, 1998, 393(6684): 440-442. [9] BARABÁSI A, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512. [10] ALBERT R, JEONG H, BARABÁSI A. Error and attack tolerance of complex networks[J]. Nature, 2000, 406(6794): 378-382. [11] COHEN R, EREZ K, BEN-AVRAHAM D, HAVLIN S. Resilience of the internet to random breakdowns[J]. Physical Review Letters, 2000, 85(21): 4626-4628. [12] COHEN R, EREZ K, BEN-AVRAHAM D, et al. Breakdown of the internet under intentional attack[J]. Physical Review Letters, 2001, 86(16): 3682. [13] FRUTOS B E, MARTÍN R A. Study of the structural and robustness characteristics of madrid metro network[J]. Sustainability, 2019, 11(12): 3486. [14] BULDYREV S V, PARSHANI R, PAUL G, et al. Catastrophic cascade of failures in interdependent networks[J]. Nature, 2010, 464(7291): 1025-1028. [15] PARSHANI R, BULDYREV S V, HAVLIN S. Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition[J]. Physical Review Letters, 2010, 105(4): 048701. [16] PARSHANI R, BULDYREV S V, HAVLIN S. Critical effect of dependency groups on the function of networks[J]. Proceedings of the National Academy of Sciences, 2011, 108(3): 1007-1010. [17] RADICCHI F. Percolation in real interdependent networks[J]. Nature Physics, 2015, 11(7): 597-602. [18] SUN S, WU Y, MA Y, et al. Impact of degree heterogeneity on attack vulnerability of interdependent networks[J]. Scientific Reports, 2016, 6: 32983. [19] BAI Y N, HUANG N, WANG L, et al. Robustness and vulnerability of networks with dynamical dependency groups[J]. Scientific Reports, 2016, 6: 37749. [20] SMOLYAK A, LEVY O, VODENSKA I, et al. Mitigation of cascading failures in complex networks[J]. Scientific Reports, 2020, 10(1): 16124. [21] TURALSKA M, SWAMI A. Greedy control of cascading failures in interdependent networks[J]. Scientific Reports, 2021, 11(1): 1-10. [22] BENSON A R, GLEICH D F, LESKOVEC J. Higher-order organization of complex networks[J]. Science, 2016, 353(6295): 163-166. [23] YIN H, BENSON A R, LESKOVEC J, et al. Local higher-order graph clustering[DB/OL].[2022-09-15].https://dl.acm.org/doi/proceedings/10.1145/3097983. [24] ROSSI R, AHMED N. The network data repository with interactive graph analytics and visualization[DB/OL].[2022-09-15].https://dl.acm.org/doi/10.5555/2888116-2888372.