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.
ZHANG Chengjun
,
YAO Hui
,
LEI Yi
,
XIA Denghui
,
LI Qi
,
SHEN Xinyu
,
QIAN Ming
,
YU Wenbin
,
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
.
DOI: 10.13306/j.1672-3813.2024.03.003
[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.