Оцінювання вразливості та відновлюваності складних мережевих та багатошарових мережевих систем
Анотація
Наведено огляд та аналіз публікацій, присвячених дослідженню проблеми уразливості реальних складних мережевих систем (МС) та процесів міжсистемних взаємодій. Здійснено загальну класифікацію типів негативних впливів, які можуть порушити структуру мережевих та багатошарових мережевих систем (БШМС) і дестабілізувати або зупинити процес їхнього функціонування. Наведено структурні та потокові моделі МС та БШМС, на основі яких визначено показники важливості елементів системи, які потребують першочергового захисту. Описано принципи побудови сценаріїв локальних, групових та загальносистемних атак на структуру та процес функціонування системи. Показано, що такі сценарії можуть бути успішно використані для протидії поширенню нецільових уражень. Запропоновано моделі оцінювання наслідків ураження структури та процесу функціонування МС та БШМС з метою розроблення стратегій їхнього найшвидшого відновлення та повернення до нормальної життєдіяльності. Проаналізовано способи оптимізації стратегій захисту реальних складних мережевих систем.
Зразок для цитування: Д. О. Поліщук, О. Д. Поліщук, М. С. Яджак, “Оцінювання вразливості та відновлюваності складних мережевих та багатошарових мережевих систем”, Мат. методи та фіз.-мех. поля, 68, No. 1-2, 174–202 (2025), https://doi.org/10.15407/mmpmf2025.68.1-2.174-202
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"17 strains of coronavirus are circulating in Ukraine – Liashko" (26 Jan 2024), Ukrinform, https://www.ukrinform.ua/rubric-health/3818861-v-ukraini-cirkulue-17-stamiv-koronavirusu-lasko.html
V. O. Val’kovs’ky, M. S. Yadzhak, “Problems of further development and modification of the pyramid method for loop parallelization,” Mat. Met. Fiz.-Mekh. Polya, 43, No. 1, 68–75 (2000) (in Ukrainian).
Yu. Holovatch, O. Olemskoi, K. fon Ferber, T. Holovatch, O. Mryglod, I. Olemskoi, V. Palchykov, “Complex networks,” Zh. Fiz. Dosl., 10, No. 4, 247–289 (2006) (in Ukrainian).
N. Grubyi, M. Yadzhak, “Application of neural networks for signal filtering,” Proc. of the Conference of Young Scientists "Pidstryhach Readings – 2025" (May 27–29, 2025, Lviv), (2025) (in Ukrainian), www.iapmm.lviv.ua/chyt2025/abstracts/Grubyi.pdf
A. M. Lutskiv, S. A. Lupenko, V. V. Pasichnyk, Parallel and Distributed Computing [in Ukrainian], Magnoliya–2006, Lviv (2024).
D. Polishchuk, O. Polishchuk, “Modified pruning process algorithm for -cores decomposition in complex networks,” Fiz.-Mat. Model. Inform. Tekh., Issue 40, 5–14 (2025) (in Ukrainian), https://doi.org/10.15407 /fmmit2025.40.005
D. O. Polishchuk, O. D. Polishchuk, M. S. Yadzhak, “Comprehensive deterministic evaluation of the complex hierarchical-network systems: I. Methods description,” Syst. Dosl.. Inform. Tekh., No. 1, 21–31 (2015) (in Ukrainian).
D. O. Polishchuk, O. D. Polishchuk, M. S. Yadzhak, “Comprehensive deterministic evaluation of the complex hierarchical-network systems: II. Local and prognostic evaluation,” Syst. Dosl. Inform. Tekh., No. 2, 26–38 (2015) (in Ukrainian).
D. O. Polishchuk, O. D. Polishchuk, M. S. Yadzhak, “Comprehensive deterministic evaluation of the complex hierarchical-network systems: III. Aggregate evaluation,” Syst. Dosl. Inform. Tekh., No. 4, 20–31 (2015) (in Ukrainian).
D. O. Polishchuk, O. D. Polishchuk, M. S. Yadzhak, “Comprehensive deterministic evaluation of the complex hierarchical-network systems: IV. Interactive evaluation,” Syst. Dosl.. Inform. Tekh., No. 1, 7–16 (2016) (in Ukrainian), https://doi.org/10.20535/SRIT.2308-8893.2016.1.01
O. D. Polishchuk, M. I. Tyutyunnyk, M. S. Yadzhak, “Quality estimation of functioning of complex systems on the base of parallel organization of calculations,” Vidbir Obr. Inform., Issue 26 (102), 121–126 (2007) (in Ukrainian).
O. D. Polishchuk, M. I. Tyutyunnyk, M. S. Yadzhak, “Organization of parallel calculations for the local estimation of quality of the complex systems functioning,” Vidbir Obr. Inform., Issue 32 (108), 119–124 (2010) (in Ukrainian).
O. D. Polishchuk, M. S. Yadzhak, “Network structures and systems: III. Hierarchies and networks,” Syst. Dosl. Inform. Tekh., No. 4, 82–95 (2018) (in Ukrainian), https://doi.org/10.20535/SRIT.2308-8893.2018.4.07
O. D. Polishchuk, M. S. Yadzhak, “Network structures and systems: IV. Parallel processing of continuous monitoring results,” Syst. Dosl. Inform. Tekh., No. 2, 105–114 (2019) (in Ukrainian), https://doi.org/10.20535/SRIT.2308-8893.2019.2.09
O. Polishchuk, M. Yadzhak, Models and Methods of Comprehensive Investigation of Complex Network Systems and Intersystem Interactions / [in Ukrainian], Pidstryhach Institute for Applied Problems of Mechanics and Mathematiics, National Academy of Sciences of Ukraine, Lviv (2023).
O. D. Polishchuk, M. S. Yadzhak, “Analysing operation efficiency of a city transportation system by the U-statistics methods. II. Optimization of the interactive evaluation methods,” Kibern. Syst. Anal., 60, No. 2, 119–127 (2024) (in Ukrainian), https://doi.org/10.34229/KCA2522-9664.24.2.10; English translation: Cybern. Syst. Anal., 60, No. 2, 268–275 (2024), https://doi.org/10.1007/s10559-024-00667-6
P. Rouch, Computational Hydrodynamics [in Russian], Mir, Moscow (1980), http://www.physics.gov.az/book_V/Rouch.pdf
I. Petrenko (ed.) Transport of Ukraine 2023: statistical collection, State Statistics Service of Ukraine, 2024 (in Ukrainian), URL: www.ukrstat.gov.ua/druk/publicat/kat_u/2024/zb/10/zb_Trans_23.pdf
M. S. Yadzhak, “Parallel algorithms for data digital filtering,” Kibern. Syst. Anal., 59, No. 1, 46–56 (2023) (in Ukrainian); English translation: Cybern. Syst. Anal., 59, No. 1, 39–48 (2023), https://doi.org/10.1007/s10559-023-00540-y
M. S. Yadzhak, O. D. Polishchuk, M. I. Tyutyunnyk, “The optimization of methods of comprehensive evaluation for complex systems on the base of parallel computations,” Inform. Mat. Met. Model., 6, No. 4, 347–356 (2016) (in Ukrainian).
M. Yadzhak, M. Tyutyunnyk, “Parallel algorithms for interactive evaluation of complex hierarchical network systems,” Fiz.-Mat. Model. Inform. Tekh., Issue 38, 141–146 (2023) (in Ukrainian).
R. K. Ahuja, T. L. Magnanti, J. B. Orlin, “Some recent advances in network flows,” SIAM Review, 33, No. 2, 175–219 (1991), https://doi.org/10.1137/1033048
R. Albert, A.-L. Barabási, “Statistical mechanics of complex networks,” Rev. Mod. Phys., 74, No. 1, Article 47 (2002), https://doi.org/10.1103/RevModPhys.74.47
R. Albert, H. Jeong, A.-L. Barabási, “Error and attack tolerance of complex networks,” Nature, 406, 378–382 (2000), https://doi.org/10.1038/35019019
L. G. Alvarez-Zuzek, M. A. Di Muro, S. Havlin, L. A. Braunstein, “Dynamic vaccination in partially overlapped multiplex network,” Phys. Rev. E., 99, No. 1, Article 012302 (2019), https://doi.org/10.1103/PhysRevE.99.012302
A. V. Anisimov, M. S. Yadzhak, “Construction of optimal algorithms for mass computations in digital filtering problems,” Kibern. Syst. Anal., 44, No. 4, 3–14 (2008) (in Russian); English translation: Cybern. Syst. Anal., 44, No. 4, 465–476 (2008), https://doi.org/10.1007/s10559-008-9018-8
A.-L. Barabasi, Linked: The New Science of Networks, MA: Perseus Books Group, Cambridge (2002).
A.-L. Barabasi, “The architecture of complexity: From network structure to human dynamics,” IEEE Control Systems, 27, No. 4, 33–42 (2007), https://doi.org/10.1109/MCS.2007.384127
A. Barrat, M. Barthélemy, R. Pastor-Satorras, A. Vespignani, “The architecture of complex weighted networks,” Proc. Natl. Acad. Sci. USA, 101, No. 11, 3747–3752 (2004), https://doi.org/10.1073/pnas.0400087101
V. Batagelj, M. Zaversnik, “An O(m) algorithm for cores decomposition of networks,” arXiv:cs/0310049 (2003), https://doi.org/10.48550/arXiv.cs/0310049
M. Bellingeri, D. Cassi, S. Vincenzi, “Efficiency of attack strategies on complex model and real-world networks,” Physica A: Stat. Mech. Appl., 414, 174–180 (2014), https://doi.org/10.1016/j.physa.2014.06.079
M. Bellingeri, M. Coscia, F. Giannotti, A. Monreale, D. Pedreschi, “Multidimensional networks: foundati¬ons of structural analysis,” Worldwide Web., Vol. 16, 567–593 (2013), https://doi.org/10.1007/s11280-012-0190-4
S. Bhattacharjee, K. Das, S. Zaman, A. Naha, A. Sadhu, S. K. Roy, F. S. Khan, B. Sarkar, “Comparative analysis of the impact of epidemiological modeling on COVID-19,” in: Computer Intelligence Against Pandemics: Tools and Methods to Face New Strains of COVID-19, de Gruyter, Berlin, Boston (2023), pp. 109–138, https://doi.org/10.1515/9783110767681-006
G. Bianconi, Multilayer Networks: Structure and Function, Oxford University Press, Oxford (2018), https://doi.org/10.1093/oso/9780198753919.001.0001
J. Bluszcz, M. Valente, “The economic costs of hybrid wars: The case of Ukraine,” Defence and Peace Economics, 33, No. 1, 1–25 (2022), https://doi.org/10.1080/10242694.2020.1791616
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, “Complex networks: Structure and dynamics,” Phys. Rep, 424, No. 4–5, 175–308 (2006), https://doi.org/10.1016/j.physrep.2005.10.009
S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, M. Zanin, “The structure and dynamics of multilayer networks,” Phys. Rep., 544, No. 1, 1–122 (2014), https://doi.org/10.1016/j.physrep.2014.07.001
S. Bornhold, H. G. Schuster, Handbook of graphs and networks: From the Genome to the Internet, Jon Wiley & Sons (2006).
N. K. Cheryala, “Systolic Arrays and the TPU,” Academia Letters, Article 1403 (2021), https://doi.org/10.20935/AL1403
M. Chessell, G. Sivakumar, D. Wolfson, K. Hogg, R. Harishankar, Common Information Models for an Open, Analytical, and Agile World, IBM Press, New York (2015).
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes, “k-Core organization of complex networks,” Phys. Rev. Lett., 96, No. 4, Article 040601 (2006), https://doi.org/10.1103/PhysRevLett.96.040601
S. N. Dorogovtsev, J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW, Oxford University Press, Oxford (2013).
E. Estrada, The Structure of Complex Networks: Theory and Applications, Oxford University Press, Oxford (2011), https://doi.org/10.1093/acprof:oso/9780199591756.001.0001
L. Glenn, “Understanding the influence of all nodes in a network,” Sci. Rep., 5, No. 1, Article 8665 (2015), https://doi.org/10.1038/srep08665
M. Gupta, R. Mishra, “Spreading the information in complex networks: Identifying a set of top-N influential nodes using network structure,” Decision Support Systems, Vol. 149, Article 113608 (2021), https://doi.org/10.1016/j.dss.2021.113608
V. Hodge, J. Austin, “A survey of outlier detection methodologies,” Artificial Intelligence Review, 22, No. 2, 85–126 (2004), https://doi.org/10.1023/B:AIRE.0000045502.10941.a9
P. Holme, B. J. Kim, C. N. Yoon, S. K. Han, “Attack vulnerability of complex networks,” Phys. Rev. E., 65, No. 5, Article 056109 (2002), https://doi.org/10.1103/PhysRevE.65.056109
P. Holme, J. Saramäki, “Temporal networks,” Phys. Rep., 519, No. 3, 97–125 (2012), https://doi.org/10.1016/j.physrep.2012.03.001
J. M. John, D. S. Lekha, “Need for a realistic measure of attack severity in centrali¬ty based node attack strategies,” In: Complex Networks and Their Applications X: Proc. of the 10th Int. Conf. on Complex Networks and Their Applications “Complex Networks–2021” (November 30 – December 2, 2021, Madrid, Spain), pp. 857–866 (2022), https://doi.org/10.1007/978-3-030-93409-5_70
I. A. Kalyaev, I. I. Levin, E. A. Semernikov, V. I. Shmoilov, Reconfigurable multipipeline computing structures, Nova Science Pub. Inc. (2013).
Y.-X. Kong, G.-Y. Shi, R.-J. Wu, Y.-C. Zhang, “k-Core: Theories and applications,” Phys. Rep., 832, 1–32 (2019), https://doi.org/10.1016/j.physrep.2019.10.004
D. Krackhardt, “Assessing the political landscape: Structure, cognition, and power in organizations,” Admin. Sci. Quart., 35, No. 2, 342–369 (1990), https://doi.org/10.2307/2393394
M. Kurant, P. Thiran, P. Hagmann, “Error and attack tolerance of layered complex networks,” Phys. Rev. E, 76, Article 026103 (2007), https://doi.org/10.1103/PhysRevE.76.026103
A. J. Lee, U-statistics: Theory and Practice, Routledge, London (2019).
B. Li, J. Springer, G. Bebis, M. H. Gunes, “A survey of network flow applications,” J. Network Comput. Appl., 36, No. 2, 567–581 (2013), https://doi.org/10.1016/j.jnca.2012.12.020
Z. Li, X. Huang, “Identifying influential spreaders in complex networks by an improved gravity model,” Sci. Rep., 11, Article 22194 (2021), https://doi.org/10.1038/s41598-021-01218-1
B. D. Lushniak, “COVID-19 caught the world unprepared,” In: Difficult Decisions in Surgical Ethics: An Evidence-Based Approach, Springer, Cham (2022), pp. 617–629, https://doi.org/10.1007/978-3-030-84625-1_44
S. Mariappan, A. D. Raj, S. Kumar, U. Chatterjee, “Global warming impacts on the environment in the last century,” In: Ecological Footprints of Climate Change: Adaptive Approaches and Sustainability, Springer, Cham (2023), pp. 63–93, https://doi.org/10.1007/978-3-031-15501-7_3
S. Mimar, Learning Dynamical Processes from Structure in Complex Networks, Dissertation, University of Rochester (2022).
R. N. Nair, F. Sunny, M. Chopra, L. K. Sharma, V. D. Puranik, A. K. Ghosh, “Estimation of radioactive leakages into the Pacific Ocean due to Fukushima nuclear accident,” Environ. Earth Sci., 71, No. 3, 1007–1019 (2014), https://doi.org/10.1007/s12665-013-2501-1
M. Newman, Networks: An Introduction, Oxford University Press, Oxford (2010).
Q. Nguyen, H. D. Pham, D. Cassi, M. Bellingeri, “Conditional attack strategy for real-world complex networks,” Phys. A Stat. Mech. Appl., 530, Article 121561 (2019), https://doi.org/10.1016/j.physa.2019.121561
R. Noldus, P. Van Mieghem, “Assortativity in complex networks,” J. Complex Netw., 3, No. 4, 507–542 (2015), https://doi.org/10.1093/comnet/cnv005
R. B. Northrop, Introduction to Complexity and Complex Systems, CRC Press, Boca Raton (2010).
F. Paganini, “A global stability result in network flow control,” Syst. Control Lett., 46, No. 3, 165–172 (2002), https://doi.org/10.1016/S0167-6911(02)00123-8
Y. Pashaei Asl, S. Ghanbari-Homaie, N. Partash, A. Pakzad, G. Faridaalaee, “Consequences of natural and man-made disasters on pregnancy outcomes and complications: A systematic review,” Arch. Acad. Emerg. Med., 12, No. 1, Article e61 (2024), https://doi.org/10.22037/aaem.v12i1.2268
M. A. F. Pimentel, D. A. Clifton, L. Clifton, L. Tarassenko, “A review of novelty detection,” Signal Processing, 99, 215–249 (2014), https://doi.org/10.1016/j.sigpro.2013.12.026
D. Polishchuk, O. Polishchuk, Flow Cores and the Problem of Vulnerability of Complex Network Systems, Research Square preprint (2025), https://doi.org/10.21203/rs.3.rs-7288855/v1
O. Polishchuk, “Influence and betweenness in flow models of complex network systems,” in T. Radivilova, D. Ageyev, N. Kryvinska (eds), Data-centric Business and Applications, Lecture Notes on Data Engineering and Communications Technologies, Vol. 48, Springer, Cham (2021), pp. 67–90, https://doi.org/10.1007/978-3-030-43070-2_5
O. Polishchuk, “Flow model of intersystem interactions and influence of components of multilayer network systems,” ArXiv: 2302.02134 [physics.soc-ph] (2023), https://doi.org/10.48550/arXiv.2302.02134
O. Polishchuk, “Communities detection in complex network and multilayer network systems: A flow approach,” arXiv:2309.11418 (2023), https://doi.org/10.48550/arXiv.2309.11418
O. Polishchuk, “Structural and flow-based approaches to vulnerability analysis of complex network systems,” in: Complex Networks and their Applications XIII, Proc. of the 13th International Conference on Complex Networks and Their Applications: Complex Networks 2024 (December 10–12, 2024, Istanbul, Turkey), Vol. 3, Springer (2025), pp. 353–365, https://doi.org/10.1007/978-3-031-82435-7_29
O. Polishchuk, “Protection of multilayer network systems from successive attacks on the process of intersystem interactions,” in: CEUR-Workshop Proceedings, Proc. of the 12th Int. Conf. Information Control Systems & Technologies (ICST–2024, September 23–25, 2024, Odesa, Ukraine), pp. 545–557, https://doi.org/10.55056/ceur-ws.org/Vol-3790/paper47.pdf
O. D. Polishchuk, “Vulnerability of complex network structures and systems,” Kibern. Syst. Anal., 56, No. 2, 166–176 (2020) (in Ukrainian); English translation: Cybern. Syst. Anal., 56, No. 2, 312–321 (2020), https://doi.org/10.1007/s10559-020-00247-4
O. Polishchuk, D. Polishchuk, “ Vulnerability of multilayer network systems to targeted group attacks,” in: CEUR-Workshop Proceedings, Proc. of the Conf. on Information Technology and Implementation (IT&I 2025, November 20–21, 2025, Kyiv, Ukraine), pp. 166–179, https://ceur-ws.org/Vol-4170/Paper14.pdf
O. Polishchuk, D. Polishchuk, “Vulnerability of multilayer network systems to sys-tem-wide disruptions,” Proc. of XXV International Scientific and Practical Confe-rence “Information Technologies and Security” (December 11, 2025, Kyiv, Ukraine), Kyiv (2025), pp. 248–251.
O. Polishchuk, M. Yadzhak, “Information and evaluation models of complex hierarchical network systems,” in: CEUR-WS, Proc. of the 2nd Int. Sci. Symp. “Intelligent Solutions” (IntSol–2021, September 28–30, 2021, Kyiv–Uzhhorod, Ukraine), pp. 21–31, https://ceur-ws.org/Vol-3106/Paper_3.pdf
P. J. Rousseeuw, A. M. Leroy, Robust regression and outlier detection, John Wiley & Sons, New York (1987).
M. Saqr, S. López-Pernas, “The curious case of centrality measures: A large-scale empirical investigation,” J. Learn. Anal., 9, No. 1, 13–31 (2022), https://doi.org/10.18608/jla.2022.7415
Y. Sawada, M. Bhattacharyay, T. Kotera, “Aggregate impacts of natural and man-made disasters: A quantitative comparison,” Int. J. Develop. Conflict., 9 (1), 43–73 (2019).
W. Sun, C. Lan, C. Yang, W. Pan, “Identification of important nodes in complex net¬works based on node and edge information,” Commun. Nonlin. Sci. Num. Simul., 152, Part A, Article 109116 (2026), https://doi.org/10.1016/j.cnsns.2025.109116
The TOP500 list, www.top500.org
O. Ugurlu, “Comparative analysis of centrality measures for identifying critical nodes in complex networks,” J. Comput. Sci., 62, Article 101738 (2022), https://doi.org/10.1016/j.jocs.2022.101738
P. A. Vitenu-Sackey, R. Barfi, “The impact of Covid-19 pandemic on the global eco¬nomy: Emphasis on poverty alleviation and economic growth,” Econ. Finance Lett., 8, No. 1, 32–43 (2021), https://doi.org/10.18488/journal.29.2021.81.32.43
Z. Wan, Y. Mahajan, B. W. Kang, T. J. Moore, J.-H. Cho, “A survey on centrality metrics and their network resilience analysis,” IEEE Access, 9, 104773–104819 (2021), https://doi.org/10.1109/ACCESS.2021.3094196
S. Wandelt, X. Sun, D. Feng, M. Zanin, S. Halvin, “A comparative analysis of approaches to network-dismantling,” Sci. Rep., 8, Article 13513 (2018), https://doi.org/10.1038/s41598-018-31902-8
X. F. Wang, G. Chen, “Complex networks: small-world, scale-free and beyond,” IEEE Circ. Syst. Mag., 3, No. 1, 6–20 (2003), https://doi.org/10.1109/MCAS.2003.1228503
Z. Wang, R. Huang, D. Yang, Y. Peng, B. Zhou, Z. Chen, “Identifying influential nodes based on the disas¬sortativity and community structure of complex network,” Sci. Rep., 14, Article 8453 (2024), https://doi.org/10.1038/s41598-024-59071-x
M. S. Yadzhak, M. I. Tyutyunnyk “An optimal algorithm to solve digital filtering problem with the use of adaptive smoothing,” Kibern. Syst. Anal., 49, No. 3, 142–151 (2013) (in Russian); English translation: Cybern. Syst. Anal., 49, No. 3, 449–456 (2013), https://doi.org/10.1007/s10559-013-9528-x
Y. Yang, T. Nishikawa, A. E. Motter, “Small vulnerable sets determine large network cascades in power grids,” Science, 358, No. 6365, Article eaan3184 (2017), https://doi.org/10.1126/science.aan3184
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