Criticality, resilience and prioritization of components in interdependent infrastructure systems: An overview of definitions and quantitative modelling approaches

Abstract

Enhancing the resilience of critical infrastructure (CI) systems has become a focal point of national and international policies. However, the formulation of resilience enhancement strategies often requires component- (i.e. asset-) level prioritization, which entails many complexities. Acknowledging the complex and interdependent nature of infrastructure systems, this paper aims to aid researchers, practitioners and policy-makers by presenting a review of the relative literature and current state-of-the-art, and by identifying future research opportunities to improve the applicability and operationalizability of CI component identification and prioritization methods. Theoretical and practical applications are reviewed for definitions, analysis and modelling approaches regarding the resilience of interdependent infrastructure systems. A detailed review of infrastructure criticality definitions, component criticality assessment and prioritization frameworks, from scientific, policy and other documents, is presented. A discussion on social justice and equity dimensions therein is included, which have the potential to greatly influence decisions and should always be incorporated in infrastructure planning and investment discussions. The findings of this review are discussed in terms of applicability and operationalizability. Key recommendations for future research include: (i) developing quantification frameworks for CI component criticality based on formal definitions and multiple criteria, (ii) incorporating the entire resilience cycle of CI in component prioritization, (iii) accounting for the socio-technical nature of CI systems by integrating social dimensions and their wider operating environment and (iv) developing comprehensive model validation, calibration and uncertainty analysis frameworks.

Keywords

Critical infrastructure / Interdependencies / Criticality / Resilience / Component importance measures / Cascading effects / System-of-systems

References

[1] Thacker S, Adshead D, Fay M, Hallegatte S, Harvey M, Meller H, O’Regan N, Rozenberg J, Watkins G, Hall JW. Infrastructure for sustainable development. Nat Sustain 2019; 2: 324-31. https://doi.org/10.1038/s41893-019-0256-8.

[2] The Economist Intelligence Unit Ltd. The critical role of infrastructure for the Sustainable Development Goals. The Economist Intelligence Unit Ltd. ; 2019. https://impact.economist.com/projects/towards-the-sdgs/pdfs/critical-role-of-infrastructure_EN.pdf [Accessed 28 October 2023].

[3] European Parliament and Council of the European Union. Directive (EU) 2022/2557 of the European Parliament and of the Council of 14 December 2022 on the resilience of critical entities and repealing Council Directive 2008/114/EC (Text with EEA relevance). 2022. http://data.europa.eu/eli/dir/2022/2557/oj/eng [Accessed 28 October 2023].

[4] The White House. National security memorandum on critical infrastructure security and resilience. 2024.

[5] Australian Government. Security of critical infrastructure act 2018. Attorney-General’s Department; 2018. https://www.legislation.gov.au/C2018A00029/latest/versions [Accessed October 28, 2023].

[6] Public Safety Canada. National strategy for critical infrastructure. Canada: Public Safety Canada ; 2009. https://www.publicsafety.gc.ca/cnt/rsrcs/pblctns/srtg-crtcl-nfrstrctr/srtg-crtcl-nfrstrctr-eng.pdf.

[7] Forzieri G, Bianchi A, e Silva FB, Marin Herrera MA, Leblois A, Lavalle C, Aerts JCJH, Feyen L. Escalating impacts of climate extremes on critical infrastructures in Europe. Glob Environ Change 2018; 48: 97-107. https://doi.org/10.1016/j.gloenvcha.2017.11.007.

[8] Verschuur J, Koks EE, Li S, Hall JW. Multi-hazard risk to global port infrastructure and resulting trade and logistics losses. Commun Earth Environ 2023; 4: 1-12. https://doi.org/10.1038/s43247-022-00656-7.

[9] Nirandjan S, Koks EE, Ye M, Pant R, Van Ginkel KCH, Aerts JCJH, Ward PJ. Review article: physical vulnerability database for critical infrastructure hazard risk assessments - a systematic review and data collection. Natur Hazards Earth Syst Sci 2024; 24: 4341-68. https://doi.org/10.5194/nhess-24-4341-2024.

[10] Masson-Delmotte V, Zhai P, Pirani A, Connors SL, Péan C, Berger S, Caud N, Chen Y, Goldfarb L, Gomis MI, Huang M, Leitzell K, Lonnoy E, Matthews JBR, Maycock TK, Waterfield T, Yelekçi Ö, Yu R, Zhou B. Climate Change 2021: the physical science basis. Contribution of working group i to the sixth assessment report of the intergovernmental panel on climate change. Cambridge, United Kingdom and New York, NY, USA: Cambridge University Press; 2021. https://doi.org/10.1017/9781009157896.

[11] AghaKouchak A, Chiang F, Huning LS, Love CA, Mallakpour I, Mazdiyasni O, Moftakhari H, Papalexiou SM, Ragno E, Sadegh M. Climate extremes and compound hazards in a warming world. Annu Rev Earth Planet Sci 2020; 48: 519- 48. https://doi.org/10.1146/annurev-earth-071719-055228.

[12] Rentschler J, Avner P, Marconcini M, Su R, Strano E, Vousdoukas M, Hallegatte S. Global evidence of rapid urban growth in flood zones since 1985. Nature 2023; 622: 87-92. https://doi.org/10.1038/s41586-023-06468-9.

[13] Werfali A, Elumami A. Libya floods wipe out quarter of city, thousands dead. Reuters; 2023. https://www.reuters.com/world/africa/more-than-1000-bodies-recovered-libyan-city-after-floods-minister-2023-09-12/ [Accessed 29 October 2023].

[14] Oughton EJ, Usher W, Tyler P, Hall JW. Infrastructure as a complex adaptive system. Complexity 2018; 2018: e3427826. https://doi.org/10.1155/2018/3427826.

[15] Rinaldi SM, Peerenboom JP, Kelly TK. Identifying, understanding, and analyzing critical infrastructure interdependencies. IEEE Control Syst Mag 2001; 21: 11-25. https://doi.org/10.1109/37.969131.

[16] Cimellaro GP. A comprehensive methodology for the evaluation of infrastructure interdependencies. In: Cimellaro GP , editor. Urban resilience for emergency response and recovery: fundamental concepts and applications. Cham: Springer International Publishing; 2016. p. 139-223. https://doi.org/10.1007/978-3-319-30656-8_7.

[17] Buldyrev SV, Parshani R, Paul G, Stanley HE, Havlin S. Catastrophic cascade of failures in interdependent networks. Nature 2010; 464: 1025-8. https://doi.org/10.1038/nature08932.

[18] Little RG. Controlling cascading failure: understanding the vulnerabilities of interconnected infrastructures. J Urban Technol 2002; 9: 109-23. https://doi.org/10.1080/106307302317379855.

[19] Rogers CDF, Bouch CJ, Williams S, Barber ARG, Baker CJ, Bryson JR, Chapman DN, Chapman L, Coaffee J, Jefferson I, Quinn AD. Resistance and resilience - paradigms for critical local infrastructure. Proc Inst Civil Eng 2012; 165: 73-83. https://doi.org/10.1680/muen.11.00030.

[20] United Nations Office for Disaster Risk Reduction (UNDRR) . Sendai framework for disaster risk reduction 2015-2030. United Nations Office for Disaster Risk Reduction (UNDRR) ; 2015. http://www.undrr.org/publication/sendai-framework-disaster-risk-reduction-2015-2030 [Accessed 29 October 2023].

[21] Rausand M, Barros A, Hoyland A. Reliability importance metrics. System reliability theory. John Wiley & Sons, Ltd; 2020. p. 299-336. https://doi.org/10.1002/9781119373940.ch7.

[22] Ouyang M. Review on modeling and simulation of interdependent critical infrastructure systems. Reliab Eng Syst Saf 2014; 121: 43-60. https://doi.org/10.1016/j.ress.2013.06.040.

[23] Iturriza M, Labaka L, Sarriegi JM, Hernantes J. Modelling methodologies for analysing critical infrastructures. J Simul 2018; 12: 128-43. https://doi.org/10.1080/17477778.2017.1418640.

[24] Griot C. Modelling and simulation for critical infrastructure interdependency assessment: a meta-review for model characterisation. IJCIS 2010; 6: 363. https://doi.org/10.1504/IJCIS.2010.037453.

[25] Chen S, Brokhausen F, Wiesner P, Hegyi D, Citir M, Huth M, Park S, Rabe J, Thamsen L, Tscheikner-Gratl F, Castelletti A, Thamsen PU, Cominola A. Coupled simulation of urban water networks and interconnected critical urban infrastructure systems: a systematic review and multi-sector research agenda. Sustain Cities Soc 2024; 104: 105283. https://doi.org/10.1016/j.scs.2024.105283.

[26] Hosseini S, Barker K, Ramirez-Marquez JE. A review of definitions and measures of system resilience. Reliab Eng Syst Saf 2016; 145: 47-61. https://doi.org/10.1016/j.ress.2015.08.006.

[27] Wied M, Oehmen J, Welo T. Conceptualizing resilience in engineering systems: an analysis of the literature. Syst Eng 2020; 23: 3-13. https://doi.org/10.1002/sys.21491.

[28] Lindbergh S, Radke J. Rethinking infrastructure network criticality for climate resilience: inputs from complexity sciences and disaster risk theory. Integrated research on disaster risks. Cham: Springer; 2021. p. 329-56. https://doi.org/10.1007/978-3-030-55563-4_18.

[29] Pursiainen C, Kytömaa E. From European critical infrastructure protection to the resilience of European critical entities: what does it mean? Sustain Resilient Infrastruct 2023; 8: 85-101. https://doi.org/10.1080/23789689.2022.2128562.

[30] Mentges A, Halekotte L, Schneider M, Demmer T, Lichte D. A resilience glossary shaped by context: reviewing resilience-related terms for critical infrastructures. Int J Disast Risk Reduct 2023; 96: 103893. https://doi.org/10.1016/j.ijdrr.2023.103893.

[31] Bruneau M, Chang SE, Eguchi RT, Lee GC, O’Rourke TD, Reinhorn AM, Shinozuka M, Tierney K, Wallace WA, von Winterfeldt D. A framework to quantitatively assess and enhance the seismic resilience of communities. Earthquake Spectra 2003; 19: 733-52. https://doi.org/10.1193/1.1623497.

[32] Linkov I, Bridges T, Creutzig F, Decker J, Fox-Lent C, Kröger W, Lambert JH, Levermann A, Montreuil B, Nathwani J, Nyer R, Renn O, Scharte B, Scheffler A, Schreurs M, Thiel-Clemen T. Changing the resilience paradigm. Nat Clim Change 2014; 4: 407-9. https://doi.org/10.1038/nclimate2227.

[33] Petersen L, Lange D, Theocharidou M. Who cares what it means? Practical reasons for using the word resilience with critical infrastructure operators. Reliab Eng Syst Saf 2020; 199: 106872. https://doi.org/10.1016/j.ress.2020.106872.

[34] Savić D. Urban Flood risk and resilience: how can we protect our cities from flooding? Hydrology 2025; 12: 78. https://doi.org/10.3390/hydrology12040078.

[35] Goessling-Reisemann S, Thier P. On the difference between risk management and resilience management for critical infrastructures. Handbook on resilience of socio-technical systems. Edward Elgar Publishing; 2019. p. 117-35. https://www.elgaronline.com/edcollchap/edcoll/9781786439369/9781786439369.00013.xml [Accessed 7 May 2024].

[36] Curt C, Tacnet J-M. Resilience of critical infrastructures: review and analysis of current approaches. Risk Anal 2018; 38: 2441-58. https://doi.org/10.1111/risa.13166.

[37] Sun W, Bocchini P, Davison BD. Resilience metrics and measurement methods for transportation infrastructure: the state of the art. Sustain Resilient Infrastruct 2020; 5: 168-99. https://doi.org/10.1080/23789689.2018.1448663.

[38] Sathurshan M, Saja A, Thamboo J, Haraguchi M, Navaratnam S. Resilience of critical infrastructure Systems: a systematic literature review of measurement frameworks. Infrastructures 2022; 7: 67. https://doi.org/10.3390/infrastructures7050067.

[39] Nan C, Sansavini G. A quantitative method for assessing resilience of interdependent infrastructures. Reliab Eng Syst Saf 2017; 157: 35-53. https://doi.org/10.1016/j.ress.2016.08.013.

[40] Argyroudis SA, Mitoulis SA, Hofer L, Zanini MA, Tubaldi E, Frangopol DM. Resilience assessment framework for critical infrastructure in a multi-hazard environment: case study on transport assets. Sci Total Environ 2020; 714: 136854. https://doi.org/10.1016/j.scitotenv.2020.136854.

[41] Kong J, Simonovic SP. Probabilistic multiple hazard resilience model of an interdependent infrastructure system. Risk Anal 2019; 39: 1843-63. https://doi.org/10.1111/risa.13305.

[42] Mitoulis S-A, Argyroudis S, Panteli M, Fuggini C, Valkaniotis S, Hynes W, Linkov I. Conflict-resilience framework for critical infrastructure peacebuilding. Sustain Cities Soc 2023; 91: 104405. https://doi.org/10.1016/j.scs.2023.104405.

[43] Linkov I, Kott A. Fundamental concepts of cyber resilience: introduction and overview. In: Kott A, Linkov I , editors. Cyber resilience of systems and networks. Cham: Springer International Publishing; 2019. p. 1-25. https://doi.org/10.1007/978-3-319-77492-3_1.

[44] Saidi S, Kattan L, Jayasinghe P, Hettiaratchi P, Taron J. Integrated infrastructure systems-a review. Sustain Cities Soc 2018; 36: 1-11. https://doi.org/10.1016/j.scs.2017.09.022.

[45] Sun W, Bocchini P, Davison BD. Overview of interdependency models of critical infrastructure for resilience assessment. Nat Hazards Rev 2022; 23: 04021058. https://doi.org/10.1061/(ASCE)NH.1527-6996.0000535.

[46] Sharma N, Nocera F, Gardoni P. Classification and mathematical modeling of infrastructure interdependencies. Sustain Resilient Infrastruct 2021; 6: 4-25. https://doi.org/10.1080/23789689.2020.1753401.

[47] Schotten R, Mühlhofer E, Chatzistefanou G-A, Bachmann D, Chen AS, Koks EE. Data for critical infrastructure network modelling of natural hazard impacts: needs and influence on model characteristics. Resilient Cities Struct 2024; 3: 55-65. https://doi.org/10.1016/j.rcns.2024.01.002.

[48] Bao-Hua Y, Li-Li X, En-Jie H. A comprehensive study method for lifeline system interaction under seismic conditions. Acta Seismol Sin 2004; 17: 211-21. https://doi.org/10.1007/BF02896935.

[49] Pederson P, Dudenhoeffer D, Hartley S, Permann M. Critical infrastructure interdependency modeling: a survey of U.S. and international research. Idaho Falls, Idaho: Idaho National Laboratory; 2006. https://doi.org/10.2172/911792.

[50] Zhang P, Peeta S. A generalized modeling framework to analyze interdependencies among infrastructure systems. Transport Res Part B 2011; 45: 553-79. https://doi.org/10.1016/j.trb.2010.10.001.

[51] Sun W, Bocchini P, Davison BD. Policy-based disaster recovery planning model for interdependent infrastructure systems under uncertainty. Struct Infrastruct Eng 2020; 17: 555-78. https://doi.org/10.1080/15732479.2020.1843504.

[52] Santella N, Steinberg LJ, Parks K. Decision making for extreme events: modeling critical infrastructure interdependencies to aid mitigation and response planning. Rev Policy Res 2009; 26: 409-22. https://doi.org/10.1111/j.1541-1338.2009.00392.x.

[53] Dudenhoeffer DD, Permann MR, Manic M. CIMS: a framework for Infrastructure Interdependency modeling and Analysis. In: Proceedings of the 2006 winter simulation conference; 2006. p. 478-85. https://doi.org/10.1109/WSC.2006.323119.

[54] Thompson JR, Frezza D, Necioglu B, Cohen ML, Hoffman K, Rosfjord K. Interdependent Critical Infrastructure Model (ICIM): an agent-based model of power and water infrastructure. Int J Critic Infrastruct Protect 2019; 24: 144-65. https://doi.org/10.1016/j.ijcip.2018.12.002.

[55] Svegrup L, Johansson J, Hassel H. Integration of critical infrastructure and societal consequence models: impact on Swedish power system mitigation decisions. Risk Anal 2019; 39: 1970-96. https://doi.org/10.1111/risa.13272.

[56] Haimes YY, Horowitz BM, Lambert JH, Santos JR, Lian C, Crowther KG. Inoperability input-output model for interdependent infrastructure sectors. I: theory and methodology. J Infrastruct Syst 2005; 11: 67-79. https://doi.org/10.1061/(ASCE)1076-0342(2005)11:2(67).

[57] Balakrishnan S, Cassottana B. InfraRisk: an open-source simulation platform for resilience analysis in interconnected power-water-transport networks. Sustain Cities Soc 2022; 83: 103963. https://doi.org/10.1016/j.scs.2022.103963.

[58] Wang F, Magoua JJ, Li N. Modeling cascading failure of interdependent critical infrastructure systems using HLA-based co-simulation. Autom Constr 2022; 133: 104008. https://doi.org/10.1016/j.autcon.2021.104008.

[59] Cimellaro GP, Malavisi M, Mahin S. Using discrete event simulation models to evaluate resilience of an emergency department. J Earthq Eng 2017; 21: 203-26. https://doi.org/10.1080/13632469.2016.1172373.

[60] Imani M, Hajializadeh D. A resilience assessment framework for critical infrastructure networks’ interdependencies. Water Sci Technol 2019; 81: 1420-31. https://doi.org/10.2166/wst.2019.367.

[61] Poljanšek K, Bono F, Gutiérrez E. Seismic risk assessment of interdependent critical infrastructure systems: the case of European gas and electricity networks. Earthq Eng Struct Dyn 2012; 41: 61-79. https://doi.org/10.1002/eqe.1118.

[62] Thacker S, Pant R, Hall JW. System-of-systems formulation and disruption analysis for multi-scale critical national infrastructures. Reliab Eng Syst Saf 2017; 167: 30-41. https://doi.org/10.1016/j.ress.2017.04.023.

[63] Alkhaleel BA. Machine learning applications in the resilience of interdependent critical infrastructure systems-a systematic literature review. Int J Critic Infrastruct Protect 2024; 44: 100646. https://doi.org/10.1016/j.ijcip.2023.100646.

[64] Auping WL, d’Hont F, Kubli MD, Slinger J, Steinmann P, van der Heijde F, van Daalen C, Pruyt E, Thissen WAH. The delft method for system dynamics. TU Delft OPEN Publishing; 2024. https://doi.org/10.59490/tb.97.

[65] Bush B, Dauelsberg L, DeLand S, LeClaire R, Powell D, Samsa M. Critical infrastructure protection decision support system (CIP/DSS) project overview. Los Alamos, New Mexico: Los Alamos National Laboratory; 2005.

[66] Cavallini S, d’Alessandro C, Volpe M, Armenia S, Carlini C, Brein E, Assogna P. A system dynamics framework for modeling critical infrastructure resilience. In: Butts J, Shenoi S, editors. Critical infrastructure protection viii. Berlin, Heidelberg: Springer; 2014. p. 141-54. https://doi.org/10.1007/978-3-662-45355-1_10.

[67] Yuan H, Yang B. System dynamics approach for evaluating the interconnection performance of Cross-Border transport infrastructure. J Manag Eng 2022; 38: 04022008. https://doi.org/10.1061/(ASCE)ME.1943-5479.0001015.

[68] Railsback SF, Grimm V. Agent-Based and individual-based modeling: a practical introduction. Princeton University Press; 2011. https://www.jstor.org/stable/j.ctt7sns7 [Accessed 7 February 2025].

[69] Aghababaei M, Koliou M. An agent-based modeling approach for community resilience assessment accounting for system interdependencies: application on education system. Eng Struct 2022; 255: 113889. https://doi.org/10.1016/j.engstruct.2022.113889.

[70] Carramiñana D, Bernardos AM, Besada JA, Casar JR. Enhancing healthcare infrastructure resilience through agent-based simulation methods. Comput Commun 2025; 234: 108070. https://doi.org/10.1016/j.comcom.2025.108070.

[71] Leontief WW. Input-output economics. Sci Am Mag 1951; 185: 15. https://doi.org/10.1038/scientificamerican1051-15.

[72] Haimes YY, Jiang P. Leontief-based model of risk in complex interconnected infrastructures. J Infrastruct Syst 2001; 7: 1-12. https://doi.org/10.1061/(ASCE)1076-0342(2001)7:1(1).

[73] Balakrishnan S, Zhang Z. Criticality and susceptibility indexes for resilience-based ranking and prioritization of components in interdependent infrastructure networks. J Manag Eng 2020; 36: 04020022. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000769.

[74] Oliva G, Panzieri S, Setola R. Fuzzy dynamic input-output inoperability model. Int J Crit Infrastruct Protect 2011; 4: 165-75. https://doi.org/10.1016/j.ijcip.2011.09.003.

[75] Oosterhaven J. On the limited usability of the inoperability IO model*. Econ Syst Res 2017; 29: 452-61. https://doi.org/10.1080/09535314.2017.1301395.

[76] Chen O, Evans B, Khoury M, Vamvakeridou-Lyroudia L, Chen AS, Mustafee N, Djordjević S, Savić DA. A hybrid simulation-based decision support system for multi-sectoral response to flooding emergency. In: Proceedings of the 19th international computing and control for the water industry conference; 2023.

[77] Gosavi A, Fraioli G, Sneed LH, Tasker N. Discrete-event-based simulation model for performance evaluation of post-earthquake restoration in a smart City. IEEE Trans Eng Manag 2020; 67: 582-92. https://doi.org/10.1109/TEM.2019.2927318.

[78] Goldsman D, Goldsman P. Discrete-event simulation. In: Loper ML, editor. Modeling and simulation in the systems engineering life cycle: core concepts and accompanying lectures. London: Springer; 2015. p. 103-9. https://doi.org/10.1007/978-1-4471-5634-5_10.

[79] Huang Y, Nikolic I. Towards a multi-model infrastructure for integrated decision-making in energy transition. In: Proceedings of the 23rd international conference on modelling and applied simulation (MAS 2024); 2024. https://doi.org/10.46354/i3m.2024.mas.002.

[80] Ahmad I, Kazmi JH, Shahzad M, Palensky P, Gawlik W. Co-simulation framework based on power system, AI and communication tools for evaluating smart grid applications. 2015 IEEE innovative smart grid technologies - Asia. ISGT ASIA; 2015. p. 1-6. https://doi.org/10.1109/ISGT-Asia.2015.7387092.

[81] Marasco S, Cardoni A, Zamani Noori A, Kammouh O, Domaneschi M, Cimellaro GP. Integrated platform to assess seismic resilience at the community level. Sustain Cities Soc 2021; 64: 102506. https://doi.org/10.1016/j.scs.2020.102506.

[82] Goodfellow I, Bengio Y, Courville A. Deep learning. MIT Press; 2016. http://www.deeplearningbook.org.

[83] Sutton RS, Barto AG. Reinforcement learning: an introduction. 2nd ed. MIT Press; 2018.

[84] Karniadakis GE, Kevrekidis IG, Lu L, Perdikaris P, Wang S, Yang L. Physics-informed machine learning. Nat Rev Phys 2021; 3: 422-40. https://doi.org/10.1038/s42254-021-00314-5.

[85] Argyroudis SA, Achillopoulou DV, Livina V, Mitoulis SA. Data-driven resilience assessment for transport infrastructure exposed to multiple hazards. Bridge maintenance, safety, management, life-cycle sustainability and innovations. CRC Press; 2021.

[86] Balakrishnan S, Cassottana B, Verma A. Application of clustering algorithms for dimensionality reduction in infrastructure resilience prediction models. Struct Infrastruct Eng 2024: 1-13. https://doi.org/10.1080/15732479.2024.2366958.

[87] Wang S, Gu X, Luan S, Zhao M. Resilience analysis of interdependent critical infrastructure systems considering deep learning and network theory. Int J Critic Infrastruct Protect 2021; 35: 100459. https://doi.org/10.1016/j.ijcip.2021.100459.

[88] Sun J, Zhang Z. A post-disaster resource allocation framework for improving resilience of interdependent infrastructure networks. Transport Res Part D 2020; 85: 102455. https://doi.org/10.1016/j.trd.2020.102455.

[89] Gautam P, Natarajan B. GNN-based criticality analysis in interconnected Infrastructure networks. In: 2024 IEEE green technologies conference (GreenTech); 2024. p. 213-7. https://doi.org/10.1109/GreenTech58819.2024.10520547.

[90] Barabási A-L. Network science. Cambridge: Cambridge University Press; 2016.

[91] Newman M. Networks. 2nd ed. Oxford: Oxford University Press; 2018. https://doi.org/10.1093/oso/9780198805090.001.0001.

[92] Albert R, Albert I, Nakarado GL. Structural vulnerability of the North American power grid. Phys Rev E 2004; 69: 025103. https://doi.org/10.1103/PhysRevE.69.025103.

[93] Shekhtman LM, Berezin Y, Danziger MM, Havlin S. Robustness of a network formed of spatially embedded networks. Phys Rev E 2014; 90: 012809. https://doi.org/10.1103/PhysRevE.90.012809.

[94] Dong S, Wang H, Mostafizi A, Song X. A network-of-networks percolation analysis of cascading failures in spatially co-located road-sewer infrastructure networks. Physica A 2020; 538: 122971. https://doi.org/10.1016/j.physa.2019.122971.

[95] Schotten R, Bachmann D. Critical infrastructure network modelling for flood risk analyses: approach and proof of concept in Accra, Ghana. J Flood Risk Manag 2023; 16: e12913. https://doi.org/10.1111/jfr3.12913.

[96] Mühlhofer E, Koks EE, Kropf CM, Sansavini G, Bresch DN. A generalized natural hazard risk modelling framework for infrastructure failure cascades. Reliab Eng Syst Saf 2023; 234: 109194. https://doi.org/10.1016/j.ress.2023.109194.

[97] Zorn C, Pant R, Thacker S, Shamseldin AY. Evaluating the magnitude and spatial extent of disruptions across interdependent national infrastructure networks. ASCE-ASME J Risk Uncert Engr Sys Part B 2020; 6. https://doi.org/10.1115/1.4046327.

[98] Poudel A, Pitilakis K, Silva V, Rao A. Infrastructure seismic risk assessment: an overview and integration to contemporary open tool towards global usage. Bull Earthq Eng 2023; 21: 4237-62. https://doi.org/10.1007/s10518-023-01693-z.

[99] Mahabadi Z, Varga L, Dolan T. A survey of multilayer networks modelled to assess robustness in infrastructure systems. Proc Inst Civil Eng 2023: 1-9. https://doi.org/10.1680/jsmic.22.00015.

[100] Bianconi G. Multilayer networks: structure and function. Oxford University Press; 2018. https://doi.org/10.1093/oso/9780198753919.001.0001.

[101] Battiston F, Nicosia V, Latora V. Structural measures for multiplex networks. Phys Rev E 2014; 89: 032804. https://doi.org/10.1103/PhysRevE.89.032804.

[102] De Domenico M. Multilayer networks: analysis and visualization: introduction to muxViz with R. Cham: Springer International Publishing; 2022. https://doi.org/10.1007/978-3-030-75718-2.

[103] Kazim M, Pirim H, Shi S, Wu D. Multilayer analysis of energy networks. Sustain Energy Grids Netw 2024; 39: 101407. https://doi.org/10.1016/j.segan.2024.101407.

[104] Ahangar NE, Sullivan KM, Nurre SG. Modeling interdependencies in infrastructure systems using multi-layered network flows. Comput Oper Res 2020; 117: 104883. https://doi.org/10.1016/j.cor.2019.104883.

[105] Baggag A, Abbar S, Zanouda T, Srivastava J. Resilience analytics: coverage and robustness in multi-modal transportation networks. EPJ Data Sci 2018; 7: 1-21. https://doi.org/10.1140/epjds/s13688-018-0139-7.

[106] Brown KA. Critical path: a brief history of critical infrastructure protection in the united states. Spectrum Publishing Group, Incorporated; 2006.

[107] Lazari A. European critical infrastructure protection. Cham: Springer International Publishing; 2014. https://doi.org/10.1007/978-3-319-07497-9.

[108] Kingdom of the Netherlands, National coordinator for counterterrorism and security (NCTV) , 2015 National Safety and Secuirty Strategy, 2015.

[109] Gallais C, Filiol E. Critical infrastructure: where do we stand today? A comprehensive and comparative study of the definitions of a Critical infrastructure. J Inf Warfare 2017; 16: 64-87.

[110] CIPedia, CIPedia Main page (n.d.). https://websites.fraunhofer.de/CIPedia/index.php/CIPedia%C2%A9_Main_Page [Accessed 17 February 2025].

[111] Steele W, Hussey K, Dovers S. What’s critical about critical infrastructure? Urban Policy Res 2017; 35: 74-86. https://doi.org/10.1080/08111146.2017.1282857.

[112] Theoharidou M, Kotzanikolaou P, Gritzalis D. Risk-based criticality analysis. In: Palmer C, Shenoi S, editors. Critical infrastructure protection III. Berlin, Heidelberg: Springer; 2009. p. 35-49. https://doi.org/10.1007/978-3-642-04798-5_3.

[113] Katina PF, Hester PT. Systemic determination of infrastructure criticality. IJCIS 2013; 9: 211. https://doi.org/10.1504/IJCIS.2013.054980.

[114] Fekete A. Common criteria for the assessment of critical infrastructures. Int J Disaster Risk Sci 2011; 2: 15-24. https://doi.org/10.1007/s13753-011-0002-y.

[115] Izuakor C, White R. Critical infrastructure Asset identification: policy, methodology and gap analysis. In: Rice M, Shenoi S, editors. Critical infrastructure protection x. Cham: Springer International Publishing; 2016. p. 27-41. https://doi.org/10.1007/978-3-319-48737-3_2.

[116] Borgovini R, Pemberton S, Rossi M. Failure mode, effects, and criticality analysis (FMECA). Rome, NY, USA: Reliability Analysis Center; 1993.

[117] ISO/IEC31010:2019 - Risk Management-Risk Assessment Techniques, (2019).

[118] Lü L, Chen D, Ren X-L, Zhang Q-M, Zhang Y-C, Zhou T. Vital nodes identification in complex networks. Phys Rep 2016; 650: 1-63. https://doi.org/10.1016/j.physrep.2016.06.007.

[119] Jafino BA , Kwakkel, Jan A, Verbraeck. Transport network criticality metrics: a comparative analysis and a guideline for selection. Transp Rev 2020; 40: 241-64. https://doi.org/10.1080/01441647.2019.1703843.

[120] J.D. Lecy, K.E. Beatty , Representative literature reviews using constrained snowball sampling and citation network analysis, (2012). https://doi.org/10.2139/ssrn.1992601.

[121] Wohlin C. Guidelines for snowballing in systematic literature studies and a replication in software engineering. In: Proceedings of the 18th international conference on evaluation and assessment in software engineering; 2014. p. 1-10. https://doi.org/10.1145/2601248.2601268.

[122] Jönsson H, Johansson J, Johansson H. Identifying critical components in technical infrastructure networks. Proc Inst Mech Eng Part O 2008; 222: 235-43. https://doi.org/10.1243/1748006XJRR138.

[123] Zio E, Sansavini G. Component criticality in failure cascade processes of network systems. Risk Anal 2011; 31: 1196-210. https://doi.org/10.1111/j.1539-6924.2011.01584.x.

[124] Latora V, Marchiori M. Vulnerability and protection of infrastructure networks. Phys Rev E 2005; 71: 015103. https://doi.org/10.1103/PhysRevE.71.015103.

[125] Theoharidou M, Kotzanikolaou P, Gritzalis D. A multi-layer criticality assessment methodology based on interdependencies. Comput Secur 2010; 29: 643-58. https://doi.org/10.1016/j.cose.2010.02.003.

[126] Fisher R, Norman M. Developing measurement indices to enhance protection and resilience of critical infrastructure and key resources. J Bus Contin Emer Plan 2010; 4: 191-206.

[127] Barker K, Ramirez-Marquez JE, Rocco CM. Resilience-based network component importance measures. Reliab Eng Syst Saf 2013; 117: 89-97. https://doi.org/10.1016/j.ress.2013.03.012.

[128] Dunn S, Wilkinson SM. Identifying critical components in infrastructure networks using network topology. J Infrastruct Syst 2013; 19: 157-65. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000120.

[129] Oh EH, Deshmukh A, Hastak M. Criticality assessment of lifeline infrastructure for enhancing disaster response. Nat Hazards Rev 2013; 14: 98-107. https://doi.org/10.1061/(ASCE)NH.1527-6996.0000084.

[130] Genge B, Kiss I, Haller P. A system dynamics approach for assessing the impact of cyber attacks on critical infrastructures. Int J Critic Infrastruct Protect 2015; 10: 3-17. https://doi.org/10.1016/j.ijcip.2015.04.001.

[131] Fang Y-P, Pedroni N, Zio E. Resilience-based component importance measures for critical infrastructure network systems. IEEE Trans Reliab 2016; 65: 502-12. https://doi.org/10.1109/TR.2016.2521761.

[132] Johansen C, Tien I. Probabilistic multi-scale modeling of interdependencies between critical infrastructure systems for resilience. Sustain Resilient Infrastruct 2018; 3: 1-15. https://doi.org/10.1080/23789689.2017.1345253.

[133] Yang S, Hu F, Thompson RG, Wang W, Li Y, Li S, Ni W. Criticality ranking for components of a transportation network at risk from tropical cyclones. Int J Disast Risk Reduct 2018; 28: 43-55. https://doi.org/10.1016/j.ijdrr.2018.02.017.

[134] Zhao C, Li N, Fang D. Criticality assessment of urban interdependent lifeline systems using a biased PageRank algorithm and a multilayer weighted directed network model. Int J Critic Infrastruct Protect 2018; 22: 100-12. https://doi.org/10.1016/j.ijcip.2018.06.002.

[135] Abdel-Mottaleb N, Ghasemi Saghand P, Charkhgard H, Zhang Q. An exact multiobjective optimization approach for evaluating water distribution infrastructure criticality and geospatial interdependence. Water Resour Res 2019; 55: 5255-76. https://doi.org/10.1029/2018WR024063.

[136] Almoghathawi Y, Barker K. Component importance measures for interdependent infrastructure network resilience. Comput Ind Eng 2019; 133: 153-64. https://doi.org/10.1016/j.cie.2019.05.001.

[137] Gómez JF, Fernández PM-G, Guillén AJ, Márquez AC. Risk-based criticality for network utilities asset management. IEEE Trans Netw Serv Manag 2019; 16: 755-68. https://doi.org/10.1109/TNSM.2019.2903985.

[138] Liu X, Ferrario E, Zio E. Identifying resilient-important elements in interdependent critical infrastructures by sensitivity analysis. Reliab Eng Syst Saf 2019; 189: 423-34. https://doi.org/10.1016/j.ress.2019.04.017.

[139] Xu Z, Ramirez-Marquez JE, Liu Y, Xiahou T. A new resilience-based component importance measure for multi-state networks. Reliab Eng Syst Saf 2020; 193: 106591. https://doi.org/10.1016/j.ress.2019.106591.

[140] Espinoza S, Poulos A, Rudnick H, de la Llera JC, Panteli M, Mancarella P. Risk and resilience assessment with component criticality ranking of electric power systems subject to earthquakes. IEEE Syst J 2020; 14: 2837-48. https://doi.org/10.1109/JSYST.2019.2961356.

[141] Rehak D, Patrman D, Brabcová V, Dvořák Z. Identifying critical elements of road infrastructure using cascading impact assessment. Transport 2020; 35: 300-14. https://doi.org/10.3846/transport.2020.12414.

[142] Karakoc DB, Barker K, Zobel CW, Almoghathawi Y. Social vulnerability and equity perspectives on interdependent infrastructure network component importance. Sustain Cities Soc 2020; 57: 102072. https://doi.org/10.1016/j.scs.2020.102072.

[143] Faramondi L, Oliva G, Setola R. Multi-criteria node criticality assessment framework for critical infrastructure networks. Int J Critic Infrastruct Protect 2020; 28: 100338. https://doi.org/10.1016/j.ijcip.2020.100338.

[144] Kay B, Lu H, Devineni P, Tabassum A, Chintavali S, Lee SM. Identification of critical infrastructure via PageRank. In: 2021 IEEE international conference on Big Data (Big Data); 2021. p. 3685-90. https://doi.org/10.1109/BigData52589.2021.9671620.

[145] Wang L, Zheng S, Wang Y, Wang L. Identification of critical nodes in multimodal transportation network. Physica A 2021; 580: 126170. https://doi.org/10.1016/j.physa.2021.126170.

[146] Almaleh A, Tipper D. Risk-based criticality assessment for smart critical infrastructures. Infrastructures 2022; 7: 3. https://doi.org/10.3390/infrastructures7010003.

[147] Li R, Gao Y. On the component resilience importance measures for infrastructure systems. Int J Critic Infrastruct Protect 2022; 36: 100481. https://doi.org/10.1016/j.ijcip.2021.100481.

[148] Blagojević N, Didier M, Stojadinović B. Quantifying component importance for disaster resilience of communities with interdependent civil infrastructure systems. Reliab Eng Syst Saf 2022; 228: 108747. https://doi.org/10.1016/j.ress.2022.108747.

[149] Šarūnienė I, Martišauskas L, Krikštolaitis R, Augutis J, Setola R. Risk assessment of critical infrastructures: a methodology based on criticality of infrastructure elements. Reliab Eng Syst Saf 2024; 243: 109797. https://doi.org/10.1016/j.ress.2023.109797.

[150] Beck AL, Cha EJ. Probabilistic disaster social impact assessment of infrastructure system nodes. Struct Infrastruct Eng 2024; 20: 421-32. https://doi.org/10.1080/15732479.2022.2097268.

[151] Alrowaili Y, Saxena N, Burnap P. Towards developing an asset-criticality identification framework in smart grids. In: 2024 IEEE international conference on cyber security and resilience (CSR); 2024. p. 720-5. https://doi.org/10.1109/CSR61664.2024.10679477.

[152] Wang F, Tian J, Ling J, Chen Z, Xu Z. A multi-stage resilience analysis framework of critical infrastructure systems based on component importance measures. Reliab Eng Syst Saf 2025; 256: 110720. https://doi.org/10.1016/j.ress.2024.110720.

[153] Chulahwat A, Hassan EM, Tariverdi M, Nunez-del-Prado M, Mahmoud H. Identifying influential assets in higher order interdependent infrastructure networks through population impact. Sci Rep 2025; 15: 33351. https://doi.org/10.1038/s41598-025-15824-w.

[154] Thomas DSK, Phillips BD, Lovekamp WE, Fothergill A. Social vulnerability to disasters. 2nd ed. Boca Raton: CRC Press; 2013. https://doi.org/10.1201/b14854.

[155] Tierney K. On risk and disaster: lessons from Hurricane Katrina. In: Daniels RJ, Kettl DF, Kunreuther H, editors. Social inequality, hazards, and disasters. University of Pennsylvania Press; 2011. p. 109-28. https://doi.org/10.9783/9780812205473.109.

[156] Coleman N, Esmalian A, Mostafavi A. Equitable resilience in infrastructure systems: empirical assessment of disparities in hardship experiences of vulnerable populations during service disruptions. Nat Hazards Rev 2020; 21: 04020034. https://doi.org/10.1061/(ASCE)NH.1527-6996.0000401.

[157] Soden R, Lallemant D, Kalirai M, Liu C, Wagenaar D, Jit S. The importance of accounting for equity in disaster risk models. Commun Earth Environ 2023; 4: 1-8. https://doi.org/10.1038/s43247-023-01039-2.

[158] Reckien D, Lwasa S, Satterthwaite D, McEvoy D, Creutzig F, Montgomery M, Schensul D, Balk D, Khan IA, et al. Equity, environmental justice, and urban climate change. In: Rosenzweig C, Solecki WD, Romero-Lankao P, Mehrotra S, Dhakal S, Ibrahim SA, editors. Climate change and cities: second assessment report of the urban climate change research network. Cambridge University Press; 2018. p. 173-224.

[159] Finucane ML, May LW, Chang J. A scoping literature review on indicators and metrics for assessing racial equity in disaster preparation, response, and recovery. RAND Corporation; 2021. https://www.rand.org/pubs/research_reports/RRA1083-1.html [Accessed 27 February 2025].

[160] McDermott M, Mahanty S, Schreckenberg K. Examining equity: a multidimensional framework for assessing equity in payments for ecosystem services. Environ Sci Policy 2013; 33: 416-27. https://doi.org/10.1016/j.envsci.2012.10.006.

[161] Climate Change 2022: impacts, adaptation and vulnerability. In: Pörtner H-O, Roberts DC, Tignor MMB, Poloczanska ES, Mintenbeck K, Alegría A, Craig M, Langsdorf S, Löschke S, Möller V, Okem A, Rama B , editors. Contribution of working group II to the sixth assessment report of the intergovernmental panel on climate change; 2022.

[162] Coleman N, Li X, Comes T, Mostafavi A. Weaving equity into infrastructure resilience research: a decadal review and future directions. Npj Nat Hazards 2024; 1: 25. https://doi.org/10.1038/s44304-024-00022-x.

[163] Lager F, Coninx I, Breil M, Bakhtaoui I, Pedersen A, Mattern K, van den Berg H, Sini E, Galluccio G, Klein R, Vierikko K. Just Resilience for Europe: towards measuring justice in climate change adaptation. ETC CA 2023. https://doi.org/10.25424/CMCC-BATP-3M95.

[164] Gunda T, Wachtel A, Khadka Mishra S, Moog E. Quantitative approaches for including equity in risk and resilience infrastructure planning analyses. Risk Anal 2025; 45: 3427-38. https://doi.org/10.1111/risa.14230.

[165] Jafino BA. An equity-based transport network criticality analysis. Transport Res Part A 2021; 144: 204-21. https://doi.org/10.1016/j.tra.2020.12.013.

[166] Yap JR, Jafino BA, Verma T. Equity principles highlight variations in road network criticality. Findings 2021. https://doi.org/10.32866/001c.24900.

[167] Cutter SL, Boruff BJ, Shirley WL. Social vulnerability to environmental hazards. Soc Sci Q 2003; 84: 242-61. https://doi.org/10.1111/1540-6237.8402002.

[168] De Plaen JJ-FG, Koks EE, Ward PJ. Towards an open pipeline for the detection of critical infrastructure from satellite imagery-a case study on electrical substations in the Netherlands. Environ Res 2024; 4: 035009. https://doi.org/10.1088/2634-4505/ad63c9.