Assessing the consequences of a disruption to complex network systems

Authors

  • Дмитро Поліщук

DOI:

https://doi.org/10.15407/fmmit2026.42.015

Keywords:

складна мережа, мережева система, уразливість, відновлюваність, цілеспрямована атака, нецільове ураження, оцінювання наслідків.

Abstract

This paper analyzes the negative impacts that can damage the structure and destabilize the functioning of a complex network system (CNS). It examines three main stages of potential impact: threat analysis and ensuring effective system protection; organizing countermeasures against the spread of the impact through the complex network; and assessing the consequences of damage and the restoration of the CNS. Based on structural and flow models of the network system, methods have been developed for the objective analysis of the consequences of negative impacts, aimed at developing effective strategies for restoring the system to normal operation. The effectiveness of the proposed approach is illustrated using examples of various types of transportation systems in Ukraine.

References

Sawada Y., Bhattacharyay M., Kotera T. Aggregate impacts of natural and man-made disasters: A quantitative comparison. International Journal of Development and Conflict, Vol. 9(1), 2019, pp. 43-73.

Polishchuk O. Structural and flow-based approaches to vulnerability analysis of complex network systems. In: Complex Networks and Their Applications XIII, Vol. 3. Springer, Cham, 2024, pp. 353-365. doi: 10.1007/978-3-031-82435-7_29. https://doi.org/10.1007/978-3-031-82435-7_29

https://doi.org/10.1007/978-3-031-82435-7_29

Wandel S. A comparative analysis of approaches to network-dismantling. Scientific Reports, Vol. 8(1), 2018, 13513. doi: 10.1038/s41598-018-31902-8. https://doi.org/10.1038/s41598-018-31902-8

https://doi.org/10.1038/s41598-018-31902-8

Barabási A.-L. Network Science. Cambridge: Cambridge University Press, 2016. doi: 10.1063/PT.3.3526. https://doi.org/10.1063/PT.3.3526

https://doi.org/10.1063/PT.3.3526

Bellingerio M., Cassi D., Vincenzi S. Efficiency of attack strategies on complex model and real-world networks. Physica A: Statistical Mechanics and its Applications, Vol. 414, 2014, pp. 174-180. doi: 10.1016/j.physa.2014.06.079. https://doi.org/10.1016/j.physa.2014.06.079

https://doi.org/10.1016/j.physa.2014.06.079

Nguyen Q. et al. Conditional attack strategy for real-world complex networks. Physica A: Statistical Mechanics and its Applications, Vol. 530, 2019, 121561. doi: 10.1016/j.physa.2019.121561. https://doi.org/10.1016/j.physa.2019.121561

https://doi.org/10.1016/j.physa.2019.121561

Glenn L. Understanding the influence of all nodes in a network. Scientific Reports, Vol. 5, 2015, 8665. doi: 10.1038/srep08665. https://doi.org/10.1038/srep08665

https://doi.org/10.1038/srep08665

Mariyam J., Lekha D.S. Need for a realistic measure of attack severity in centrality based node attack strategies. In: Complex Networks and Their Applications XI. Springer, Cham, 2022, pp. 857-866. https://doi.org/10.1007/978-3-030-93409-5_70

https://doi.org/10.1007/978-3-030-93409-5_70

Polishchuk O., Yadzhak M. Models and methods of complex study of complex network systems and intersystem interactions. Lviv: Institute of Applied Problems of Mechanics and Mathematics named after Ya.S. Pidstryhach of NAS of Ukraine, 2023.

Sun W. et al. Identification of important nodes in complex networks based on node and edge information. Communications in Nonlinear Science and Numerical Simulation, Vol. 152, 2025, 109116. doi: 10.1016/j.cnsns.2025.109116. https://doi.org/10.1016/j.cnsns.2025.109116

https://doi.org/10.1016/j.cnsns.2025.109116

Wan Z. et al. A survey on centrality metrics and their network resilience analysis. IEEE Access, Vol. 9, 2021, pp. 104773-104819. doi: 10.1109/ACCESS.2021.3094196. https://doi.org/10.1109/ACCESS.2021.3094196

https://doi.org/10.1109/ACCESS.2021.3094196

Polishchuk O., Polishchuk D. Protection of multilayer network systems from targeted group attacks. arXiv:2503.20269, 2025. doi: 10.48550/arXiv.2503.20269. https://doi.org/10.32388/RH65Y6

Polishchuk O., Polishchuk D. Vulnerability of multilayer network systems to system-wide lesions. arXiv:2503.21161, 2025. doi: 10.48550/arXiv.2503.21161.

Polishchuk O. Protection of multilayer network systems from successive attacks on the process of intersystem interactions. CEUR-WS, Vol. 3790, 2024, pp. 545-557.

https://doi.org/10.32388/RH65Y6

Yang Y., Nishikawa T., Motter A.E. Small vulnerable sets determine large network cascades in power grids. Science, Vol. 358(6365), 2017, eaan3184. doi: 10.1126/science.aan3184. https://doi.org/10.1126/science.aan3184

https://doi.org/10.1126/science.aan3184

Boccaletti S. et al. Complex networks: Structure and dynamics. Physics Reports, Vol. 424(4), 2006, pp. 175-308. doi: 10.1016/j.physrep.2005.10.009. https://doi.org/10.1016/j.physrep.2005.10.009

https://doi.org/10.1016/j.physrep.2005.10.009

Mimar S. Learning Dynamical Processes from Structure in Complex Networks. Rochester: University of Rochester, 2022.

Barrat A. et al. The architecture of complex weighted networks. PNAS, Vol. 101(11), 2004, pp. 3747-3752. doi: 10.1073/pnas.0400087101. https://doi.org/10.1073/pnas.0400087101

https://doi.org/10.1073/pnas.0400087101

Barabási A.-L. The architecture of complexity. IEEE Control Systems Magazine, Vol. 27(4), 2007, pp. 33-42. doi: 10.1109/MCS.2007.384127. https://doi.org/10.1109/MCS.2007.384127

https://doi.org/10.1109/MCS.2007.384127

Polishchuk O. Vulnerability of complex network structures and systems. Cybernetics and Systems Analysis, Vol. 56(2), 2020, pp. 312-321. doi: 10.1007/s10559-020-00247-4. https://doi.org/10.1007/s10559-020-00247-4

https://doi.org/10.1007/s10559-020-00247-4

Transport Ukrainy [Transport of Ukraine]. State Statistics Service of Ukraine, 2024. https://www.ukrstat.gov.ua/druk/publicat/kat_u/2024/zb/10/zb_Trans_23.pdf

Ugurlu O. Comparative analysis of centrality measures for identifying critical nodes in complex networks. Journal of Computational Science, Vol. 62, 2022, 101738. doi: 10.1016/j.jocs.2022.101738. https://doi.org/10.1016/j.jocs.2022.101738

https://doi.org/10.1016/j.jocs.2022.101738

Noldus R., Van Mieghem P. Assortativity in complex networks. Journal of Complex Networks, Vol. 3(4), 2015, pp. 507-542. doi: 10.1093/comnet/cnv005. https://doi.org/10.1093/comnet/cnv005

Published

2026-06-18 — Updated on 2026-06-18

How to Cite

Поліщук, Д. (2026). Assessing the consequences of a disruption to complex network systems. PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, (42), 15–25. https://doi.org/10.15407/fmmit2026.42.015