MULTIGRAPH MODELLING OF INTERRELATIONS IN THE DIGITAL MANAGEMENT SYSTEM OF AN ENTREPRENEURIAL STRUCTURE
Keywords:
digital twin, multigraph, management model, entrepreneurial structure, digital transformation, weight coefficient, scenario modelling
Abstract
The article addresses the transition of entrepreneurial structures from the fragmented digitalisation of individual functions to an integrated digital management loop. The relevance of the topic follows from a persistent asymmetry: enterprises accumulate a considerable volume of digital data and tools, while managerial decisions are still taken within isolated functional circuits, although virtually every significant decision generates cross-functional consequences. The purpose of the study is to develop a formalised toolkit for assessing the cross-functional consequences of managerial decisions prior to their implementation on the basis of an enterprise digital twin system. The methodological basis combines a systems approach to the enterprise as a multilevel socio-economic system, typological analysis, the formal apparatus of multilayer networks, formalisation and scenario modelling with a numerical illustration. It is shown that a digital twin should be treated not as a technological replica of a single asset, but as a management loop combining factual data, a digital representation of business processes, analytics, scenario modelling and decision-making. Five types of digital twins are distinguished – operational, financial-economic, organisational, market and strategic – and eight types of links between the elements of the management system. The multigraph model MG = {V, E, L, W, T} is formalised, in which links differ by type, weight coefficient and time layer, and its place in the seven-level architecture of the integrated digital management model is defined. An aggregate influence index is proposed that convolves the weights of the paths from the source node of a managerial event to the receiving node. A numerical example of the supply delay scenario demonstrates the mechanism for assessing cross-functional consequences: an increase in the weight of the risk link from 0.41 to 0.74 translates into a 35.4 % increase in the unnormalised aggregate influence index of the Costs node, while the risk channel turns from secondary into dominant. The practical value of the results lies in the possibility of using the model as the analytical core of decision support systems, which allows managerial attention to be distributed between functional circuits before actual losses occur.
References
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10. IT-Enterprise. Digital grain elevator: NIBULON agricultural company reboots quantitative and qualitative accounting processes with IT-Enterprise platform. 2025. URL: https://www.it.ua/en/news/cifrovij-elevator-na-platformi-it-enterprise-agrokompanija-nibulon-perezavantazhila-procesi-kilkisno-jakisnogo-obliku
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15. NIBULON. NIBULON overhauls quantitative and qualitative accounting processes on the IT-Enterprise platform. 2025. URL: https://www.nibulon.com/en/nibulon-overhauls-quantitative-and-qualitative-accounting-processes-on-the-it-enterprise-platform/
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17. Qi Q., Tao F. Digital twin and big data towards smart manufacturing and Industry 4.0: 360 degree comparison. IEEE Access. 2018. Vol. 6. P. 3585–3593. DOI: https://doi.org/10.1109/ACCESS.2018.2793265
18. Semeraro C., Lezoche M., Panetto H., Dassisti M. Digital twin paradigm: A systematic literature review. Computers in Industry. 2021. Vol. 130. Art. 103469. DOI: https://doi.org/10.1016/j.compind.2021.103469
19. Tao F., Qi Q., Wang L., Nee A. Digital twins and cyber-physical systems toward smart manufacturing and Industry 4.0: Correlation and comparison. Engineering. 2019. Vol. 5, № 4. P. 653–661. DOI: https://doi.org/10.1016/j.eng.2019.01.014
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1. Blahodyr, L. (2022). Tsyfrovi biznes-ekosystemy yak spetsyfichna forma koordynatsii hospodarskoi diialnosti v umovakh tsyfrovoi ekonomiky [Digital business ecosystems as a specific form of coordination of economic activity in the digital economy]. Ekonomika ta suspilstvo, no. 46. DOI: https://doi.org/10.32782/2524-0072/2022-46-55 (in Ukrainian)
2. Buhrimenko, R., & Smirnova, P. (2024). Vplyv rozvytku tsyfrovoi transformatsii na diialnist pidpryiemstva [The impact of digital transformation development on enterprise activity]. Ekonomika ta suspilstvo, no. 59. DOI: https://doi.org/10.32782/2524-0072/2024-59-29 (in Ukrainian)
3. Bulat, V. L., Mykolenko, R. O., & Dyma, O. O. (2025). Tsyfrova transformatsiia biznes-protsesiv: osoblyvosti ta peredumovy vynyknennia [Digital transformation of business processes: features and prerequisites]. Ekonomika. Menedzhment. Biznes, no. 3, pp. 4–10. DOI: https://doi.org/10.31673/2415-8089.2025.030110 (in Ukrainian)
4. Grynko, T., & Duliepov, S. (2025). Teoretychni osnovy formuvannia alhorytmu rozvytku biznes-struktur v umovakh minlyvoho pidpryiemnytskoho seredovyshcha [Theoretical foundations of forming a business structures development algorithm in a changing entrepreneurial environment]. Ekonomika ta suspilstvo, no. 77. DOI: https://doi.org/10.32782/2524-0072/2025-77-62 (in Ukrainian)
5. Acemoglu, D., Carvalho, V. M., Ozdaglar, A., & Tahbaz-Salehi, A. (2012). The network origins of aggregate fluctuations. Econometrica, vol. 80, no. 5, pp. 1977–2016. DOI: https://doi.org/10.3982/ECTA9623
6. Barricelli, B. R., Casiraghi, E., & Fogli, D. (2019). A survey on digital twin: Definitions, characteristics, applications, and design implications. IEEE Access, vol. 7, pp. 167653–167671. DOI: https://doi.org/10.1109/ACCESS.2019.2953499
7. Battiston, F., Nicosia, V., & Latora, V. (2014). Structural measures for multiplex networks. Physical Review E, vol. 89, no. 3, art. 032804. DOI: https://doi.org/10.1103/PhysRevE.89.032804
8. Fuller, A., Fan, Z., Day, C., & Barlow, C. (2020). Digital Twin: Enabling technologies, challenges and open research. IEEE Access, vol. 8, pp. 108952–108971. DOI: https://doi.org/10.1109/ACCESS.2020.2998358
9. Grieves, M., & Vickers, J. (2017). Digital Twin: Mitigating unpredictable, undesirable emergent behavior in complex systems. In Transdisciplinary Perspectives on Complex Systems, pp. 85–113. Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-38756-7_4
10. IT-Enterprise (2025). Digital grain elevator: NIBULON agricultural company reboots quantitative and qualitative accounting processes with IT-Enterprise platform. Available at: https://www.it.ua/en/news/cifrovij-elevator-na-platformi-it-enterprise-agrokompanija-nibulon-perezavantazhila-procesi-kilkisno-jakisnogo-obliku
11. Jones, D., Snider, C., Nassehi, A., Yon, J., & Hicks, B. (2020). Characterising the Digital Twin: A systematic literature review. CIRP Journal of Manufacturing Science and Technology, vol. 29, pp. 36–52. DOI: https://doi.org/10.1016/j.cirpj.2020.02.002
12. Karabulut, E., Pileggi, S. F., Groth, P., & Degeler, V. (2024). Ontologies in digital twins: A systematic literature review. Future Generation Computer Systems, vol. 153, pp. 442–456. DOI: https://doi.org/10.1016/j.future.2023.12.013
13. Kritzinger, W., Karner, M., Traar, G., Henjes, J., & Sihn, W. (2018). Digital Twin in manufacturing: A categorical literature review and classification. IFAC-PapersOnLine, vol. 51, no. 11, pp. 1016–1022. DOI: https://doi.org/10.1016/j.ifacol.2018.08.474
14. Latifundist.com (2025). NIBULON’s digital twin project pays off in less than a year. Available at: https://latifundist.com/en/novosti/68641-nibulon-okupiv-investitsiyi-u-tsifrovogo-dvijnika-elevatoriv-menshe-nizh-za-rik
15. NIBULON (2025). NIBULON overhauls quantitative and qualitative accounting processes on the IT-Enterprise platform. Available at: https://www.nibulon.com/en/nibulon-overhauls-quantitative-and-qualitative-accounting-processes-on-the-it-enterprise-platform/
16. NIBULON (2025). Investments in the elevator digital twin paid off in less than a year. Available at: https://www.nibulon.com/en/investments-in-the-elevator-digital-twin-paid-off-in-less-than-a-year/
17. Qi, Q., & Tao, F. (2018). Digital twin and big data towards smart manufacturing and Industry 4.0: 360 degree comparison. IEEE Access, vol. 6, pp. 3585–3593. DOI: https://doi.org/10.1109/ACCESS.2018.2793265
18. Semeraro, C., Lezoche, M., Panetto, H., & Dassisti, M. (2021). Digital twin paradigm: A systematic literature review. Computers in Industry, vol. 130, art. 103469. DOI: https://doi.org/10.1016/j.compind.2021.103469
19. Tao, F., Qi, Q., Wang, L., & Nee, A. (2019). Digital twins and cyber-physical systems toward smart manufacturing and Industry 4.0: Correlation and comparison. Engineering, vol. 5, no. 4, pp. 653–661. DOI: https://doi.org/10.1016/j.eng.2019.01.014
20. Tao, F., Zhang, H., Liu, A., & Nee, A. (2019). Digital twin in industry: State-of-the-art. IEEE Transactions on Industrial Informatics, vol. 15, no. 4, pp. 2405–2415. DOI: https://doi.org/10.1109/TII.2018.2873186
2. Бугріменко Р., Смірнова П. Вплив розвитку цифрової трансформації на діяльність підприємства. Економіка та суспільство. 2024. Вип. 59. DOI: https://doi.org/10.32782/2524-0072/2024-59-29
3. Булат В. Л., Миколенко Р. О., Дима О. О. Цифрова трансформація бізнес-процесів: особливості та передумови виникнення. Економіка. Менеджмент. Бізнес. 2025. № 3. С. 4–10. DOI: https://doi.org/10.31673/2415-8089.2025.030110
4. Гринько Т., Дулєпов С. Теоретичні основи формування алгоритму розвитку бізнес-структур в умовах мінливого підприємницького середовища. Економіка та суспільство. 2025. Вип. 77. DOI: https://doi.org/10.32782/2524-0072/2025-77-62
5. Acemoglu D., Carvalho V. M., Ozdaglar A., Tahbaz-Salehi A. The network origins of aggregate fluctuations. Econometrica. 2012. Vol. 80, № 5. P. 1977–2016. DOI: https://doi.org/10.3982/ECTA9623
6. Barricelli B. R., Casiraghi E., Fogli D. A survey on digital twin: Definitions, characteristics, applications, and design implications. IEEE Access. 2019. Vol. 7. P. 167653–167671. DOI: https://doi.org/10.1109/ACCESS.2019.2953499
7. Battiston F., Nicosia V., Latora V. Structural measures for multiplex networks. Physical Review E. 2014. Vol. 89, № 3. Art. 032804. DOI: https://doi.org/10.1103/PhysRevE.89.032804
8. Fuller A., Fan Z., Day C., Barlow C. Digital Twin: Enabling Technologies, Challenges and Open Research. IEEE Access. 2020. Vol. 8. P. 108952–108971. DOI: https://doi.org/10.1109/ACCESS.2020.2998358
9. Grieves M., Vickers J. Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems. Transdisciplinary Perspectives on Complex Systems. Cham : Springer, 2017. P. 85–113. DOI: https://doi.org/10.1007/978-3-319-38756-7_4
10. IT-Enterprise. Digital grain elevator: NIBULON agricultural company reboots quantitative and qualitative accounting processes with IT-Enterprise platform. 2025. URL: https://www.it.ua/en/news/cifrovij-elevator-na-platformi-it-enterprise-agrokompanija-nibulon-perezavantazhila-procesi-kilkisno-jakisnogo-obliku
11. Jones D., Snider C., Nassehi A., Yon J., Hicks B. Characterising the Digital Twin: A systematic literature review. CIRP Journal of Manufacturing Science and Technology. 2020. Vol. 29. P. 36–52. DOI: https://doi.org/10.1016/j.cirpj.2020.02.002
12. Karabulut E., Pileggi S. F., Groth P., Degeler V. Ontologies in digital twins: A systematic literature review. Future Generation Computer Systems. 2024. Vol. 153. P. 442–456. DOI: https://doi.org/10.1016/j.future.2023.12.013
13. Kritzinger W., Karner M., Traar G., Henjes J., Sihn W. Digital Twin in manufacturing: A categorical literature review and classification. IFAC-PapersOnLine. 2018. Vol. 51, № 11. P. 1016–1022. DOI: https://doi.org/10.1016/j.ifacol.2018.08.474
14. Latifundist.com. NIBULON’s digital twin project pays off in less than a year. 2025. URL: https://latifundist.com/en/novosti/68641-nibulon-okupiv-investitsiyi-u-tsifrovogo-dvijnika-elevatoriv-menshe-nizh-za-rik
15. NIBULON. NIBULON overhauls quantitative and qualitative accounting processes on the IT-Enterprise platform. 2025. URL: https://www.nibulon.com/en/nibulon-overhauls-quantitative-and-qualitative-accounting-processes-on-the-it-enterprise-platform/
16. NIBULON. Investments in the elevator digital twin paid off in less than a year. 2025. URL: https://www.nibulon.com/en/investments-in-the-elevator-digital-twin-paid-off-in-less-than-a-year/
17. Qi Q., Tao F. Digital twin and big data towards smart manufacturing and Industry 4.0: 360 degree comparison. IEEE Access. 2018. Vol. 6. P. 3585–3593. DOI: https://doi.org/10.1109/ACCESS.2018.2793265
18. Semeraro C., Lezoche M., Panetto H., Dassisti M. Digital twin paradigm: A systematic literature review. Computers in Industry. 2021. Vol. 130. Art. 103469. DOI: https://doi.org/10.1016/j.compind.2021.103469
19. Tao F., Qi Q., Wang L., Nee A. Digital twins and cyber-physical systems toward smart manufacturing and Industry 4.0: Correlation and comparison. Engineering. 2019. Vol. 5, № 4. P. 653–661. DOI: https://doi.org/10.1016/j.eng.2019.01.014
20. Tao F., Zhang H., Liu A., Nee A. Digital twin in industry: State-of-the-art. IEEE Transactions on Industrial Informatics. 2019. Vol. 15, № 4. P. 2405–2415. DOI: https://doi.org/10.1109/TII.2018.2873186
1. Blahodyr, L. (2022). Tsyfrovi biznes-ekosystemy yak spetsyfichna forma koordynatsii hospodarskoi diialnosti v umovakh tsyfrovoi ekonomiky [Digital business ecosystems as a specific form of coordination of economic activity in the digital economy]. Ekonomika ta suspilstvo, no. 46. DOI: https://doi.org/10.32782/2524-0072/2022-46-55 (in Ukrainian)
2. Buhrimenko, R., & Smirnova, P. (2024). Vplyv rozvytku tsyfrovoi transformatsii na diialnist pidpryiemstva [The impact of digital transformation development on enterprise activity]. Ekonomika ta suspilstvo, no. 59. DOI: https://doi.org/10.32782/2524-0072/2024-59-29 (in Ukrainian)
3. Bulat, V. L., Mykolenko, R. O., & Dyma, O. O. (2025). Tsyfrova transformatsiia biznes-protsesiv: osoblyvosti ta peredumovy vynyknennia [Digital transformation of business processes: features and prerequisites]. Ekonomika. Menedzhment. Biznes, no. 3, pp. 4–10. DOI: https://doi.org/10.31673/2415-8089.2025.030110 (in Ukrainian)
4. Grynko, T., & Duliepov, S. (2025). Teoretychni osnovy formuvannia alhorytmu rozvytku biznes-struktur v umovakh minlyvoho pidpryiemnytskoho seredovyshcha [Theoretical foundations of forming a business structures development algorithm in a changing entrepreneurial environment]. Ekonomika ta suspilstvo, no. 77. DOI: https://doi.org/10.32782/2524-0072/2025-77-62 (in Ukrainian)
5. Acemoglu, D., Carvalho, V. M., Ozdaglar, A., & Tahbaz-Salehi, A. (2012). The network origins of aggregate fluctuations. Econometrica, vol. 80, no. 5, pp. 1977–2016. DOI: https://doi.org/10.3982/ECTA9623
6. Barricelli, B. R., Casiraghi, E., & Fogli, D. (2019). A survey on digital twin: Definitions, characteristics, applications, and design implications. IEEE Access, vol. 7, pp. 167653–167671. DOI: https://doi.org/10.1109/ACCESS.2019.2953499
7. Battiston, F., Nicosia, V., & Latora, V. (2014). Structural measures for multiplex networks. Physical Review E, vol. 89, no. 3, art. 032804. DOI: https://doi.org/10.1103/PhysRevE.89.032804
8. Fuller, A., Fan, Z., Day, C., & Barlow, C. (2020). Digital Twin: Enabling technologies, challenges and open research. IEEE Access, vol. 8, pp. 108952–108971. DOI: https://doi.org/10.1109/ACCESS.2020.2998358
9. Grieves, M., & Vickers, J. (2017). Digital Twin: Mitigating unpredictable, undesirable emergent behavior in complex systems. In Transdisciplinary Perspectives on Complex Systems, pp. 85–113. Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-38756-7_4
10. IT-Enterprise (2025). Digital grain elevator: NIBULON agricultural company reboots quantitative and qualitative accounting processes with IT-Enterprise platform. Available at: https://www.it.ua/en/news/cifrovij-elevator-na-platformi-it-enterprise-agrokompanija-nibulon-perezavantazhila-procesi-kilkisno-jakisnogo-obliku
11. Jones, D., Snider, C., Nassehi, A., Yon, J., & Hicks, B. (2020). Characterising the Digital Twin: A systematic literature review. CIRP Journal of Manufacturing Science and Technology, vol. 29, pp. 36–52. DOI: https://doi.org/10.1016/j.cirpj.2020.02.002
12. Karabulut, E., Pileggi, S. F., Groth, P., & Degeler, V. (2024). Ontologies in digital twins: A systematic literature review. Future Generation Computer Systems, vol. 153, pp. 442–456. DOI: https://doi.org/10.1016/j.future.2023.12.013
13. Kritzinger, W., Karner, M., Traar, G., Henjes, J., & Sihn, W. (2018). Digital Twin in manufacturing: A categorical literature review and classification. IFAC-PapersOnLine, vol. 51, no. 11, pp. 1016–1022. DOI: https://doi.org/10.1016/j.ifacol.2018.08.474
14. Latifundist.com (2025). NIBULON’s digital twin project pays off in less than a year. Available at: https://latifundist.com/en/novosti/68641-nibulon-okupiv-investitsiyi-u-tsifrovogo-dvijnika-elevatoriv-menshe-nizh-za-rik
15. NIBULON (2025). NIBULON overhauls quantitative and qualitative accounting processes on the IT-Enterprise platform. Available at: https://www.nibulon.com/en/nibulon-overhauls-quantitative-and-qualitative-accounting-processes-on-the-it-enterprise-platform/
16. NIBULON (2025). Investments in the elevator digital twin paid off in less than a year. Available at: https://www.nibulon.com/en/investments-in-the-elevator-digital-twin-paid-off-in-less-than-a-year/
17. Qi, Q., & Tao, F. (2018). Digital twin and big data towards smart manufacturing and Industry 4.0: 360 degree comparison. IEEE Access, vol. 6, pp. 3585–3593. DOI: https://doi.org/10.1109/ACCESS.2018.2793265
18. Semeraro, C., Lezoche, M., Panetto, H., & Dassisti, M. (2021). Digital twin paradigm: A systematic literature review. Computers in Industry, vol. 130, art. 103469. DOI: https://doi.org/10.1016/j.compind.2021.103469
19. Tao, F., Qi, Q., Wang, L., & Nee, A. (2019). Digital twins and cyber-physical systems toward smart manufacturing and Industry 4.0: Correlation and comparison. Engineering, vol. 5, no. 4, pp. 653–661. DOI: https://doi.org/10.1016/j.eng.2019.01.014
20. Tao, F., Zhang, H., Liu, A., & Nee, A. (2019). Digital twin in industry: State-of-the-art. IEEE Transactions on Industrial Informatics, vol. 15, no. 4, pp. 2405–2415. DOI: https://doi.org/10.1109/TII.2018.2873186
Published
2026-10-29
How to Cite
Bazyk, O., & Grynko, T. (2026). MULTIGRAPH MODELLING OF INTERRELATIONS IN THE DIGITAL MANAGEMENT SYSTEM OF AN ENTREPRENEURIAL STRUCTURE. Entrepreneurship and Innovation, (42), 9-16. https://doi.org/10.32782/2415-3583/42.1
Section
ARTICLES
Copyright (c) 2026 О.В. Базик, Т.В. Гринько
This work is licensed under a Creative Commons Attribution 4.0 International License.
