Leveraging Network Theory and Stress Tests to Assess Interdependencies in Critical Infrastructures

  • Luca Galbusera
  • Georgios GiannopoulosEmail author
Part of the Advanced Sciences and Technologies for Security Applications book series (ASTSA)


Many modern critical infrastructures manifest reciprocal dependencies at various levels and on a time-evolving scale. Network theory has been exploited in the last decades to achieve a better understanding of topologies, correlations and propagation paths in case of perturbations. The discipline is providing interesting insights into aspects such as fragility and robustness of different network layouts against various types of threats, despite the difficulties arising in the modeling of the associated processes and entity relationships. Indeed, the evolution of infrastructures is not, in general, the straightforward outcome of a comprehensive a priori design. Rather, factors such as societal priorities, technical and budgetary constraints, critical events and the quest for better and cost-effective services induce a continuous change, while new kinds of interdependencies emerge. As a consequence, mapping emerging behavior can constitute a challenge and promote the development of innovative approaches to analysis and management. Among them, stress tests are entering the stage in order to assess networked infrastructures and reveal the associated operational boundaries and risk exposures. In this chapter, we first overview key developments of network science and its applications to primary infrastructure sectors. Secondly, we address the implementation of network-theoretical concepts in actions related to resilience enhancement, referring in particular to the case of stress tests in the banking sector. Finally, a discussion on the relevance of those concepts to critical infrastructure governance is provided.


Critical infrastructures Network theory Stress tests Interdependencies Resilience 


  1. 1.
    Acemoglu D, Ozdaglar A, Tahbaz-Salehi A (2015) Systemic risk and stability in financial networks. Am Econ Rev 105(2):564–608CrossRefGoogle Scholar
  2. 2.
    Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Albert R, Jeong H, Barabási AL (1999) Internet: diameter of the world-wide web. Nature 401(6749):130CrossRefGoogle Scholar
  4. 4.
    Albert R, Jeong H, Barabási AL (2000) Error and attack tolerance of complex networks. Nature 406(6794):378–382CrossRefGoogle Scholar
  5. 5.
    Albert R, Albert I, Nakarado GL (2004) Structural vulnerability of the north american power grid. Phys Rev E 69(2):025103CrossRefGoogle Scholar
  6. 6.
    Aldasoro I, Alves I (2018) Multiplex interbank networks and systemic importance: an application to European data. J Financ Stab 35:17–37CrossRefGoogle Scholar
  7. 7.
    Allen F, Babus A (2009) Networks in finance. The network challenge: strategy, profit, and risk in an interlinked world, vol 367. Wharton School, Upper Saddle RiverGoogle Scholar
  8. 8.
    Amaral LAN, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci 97(21):11149–11152CrossRefGoogle Scholar
  9. 9.
    Ancillotti E, Bruno R, Conti M (2013) The role of communication systems in smart grids: architectures, technical solutions and research challenges. Comput Commun 36(17–18):1665–1697CrossRefGoogle Scholar
  10. 10.
    Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Bargigli L, Di Iasio G, Infante L, Lillo F, Pierobon F (2015) The multiplex structure of interbank networks. Quant Finan 15(4):673–691MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Barrat A, Barthelemy M, Vespignani A (2007) The architecture of complex weighted networks: measurements and models. In: Caldarelli G, Vespignani A (eds) Large scale structure and dynamics of complex networks: from information technology to finance and natural science, pp 67–92. World Scientific, SingaporeCrossRefGoogle Scholar
  13. 13.
    Barrat A, Barthelemy M, Vespignani A (2008) Dynamical processes on complex networks, vol 1. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  14. 14.
    Barthélemy M (2011) Spatial networks. Phys Rep 499(1–3):1–101MathSciNetCrossRefGoogle Scholar
  15. 15.
    Barthelemy M (2017) Morphogenesis of spatial networks. Springer, ChamzbMATHGoogle Scholar
  16. 16.
    Battiston S, Puliga M, Kaushik R, Tasca P, Caldarelli G (2012) Debtrank: too central to fail? Financial networks, the fed and systemic risk. Sci Rep 2:541CrossRefGoogle Scholar
  17. 17.
    Battiston S, Caldarelli G, D’Errico M, Gurciullo S (2016) Leveraging the network: a stress-test framework based on debtrank. Stat Risk Model 33(3–4):117–138MathSciNetzbMATHGoogle Scholar
  18. 18.
    Battiston S, Farmer JD, Flache A, Garlaschelli D, Haldane AG, Heesterbeek H, Hommes C, Jaeger C, May R, Scheffer M (2016) Complexity theory and financial regulation. Science 351(6275):818–819CrossRefGoogle Scholar
  19. 19.
    Battiston S, Mandel A, Monasterolo I, Schütze F, Visentin G (2017) A climate stress-test of the financial system. Nat Clim Chang 7(4):283CrossRefGoogle Scholar
  20. 20.
    Bech ML, Atalay E (2010) The topology of the federal funds market. Physica A Stat Mech Appl 389(22):5223–5246CrossRefGoogle Scholar
  21. 21.
    Boccaletti S, Bianconi G, Criado R, Del Genio CI, Gómez-Gardenes J, Romance M, Sendina-Nadal I, Wang Z, Zanin M (2014) The structure and dynamics of multilayer networks. Phys Rep 544(1):1–122MathSciNetCrossRefGoogle Scholar
  22. 22.
    Bollobás B (1998) Random graphs. In: Bollobás B (ed) Modern graph theory, pp 215–252. Springer, New YorkzbMATHCrossRefGoogle Scholar
  23. 23.
    Bollobás B (1998) Modern graph theory, vol 184. Springer Verlag, New YorkzbMATHGoogle Scholar
  24. 24.
    Bollobás BE, Riordan O, Spencer J, Tusnády G (2001) The degree sequence of a scale-free random graph process. Random Struct Algoritm 18(3):279–290MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Borio C, Drehmann M, Tsatsaronis K (2014) Stress-testing macro stress testing: does it live up to expectations? J Financ Stab 12:3–15CrossRefGoogle Scholar
  26. 26.
    Boss M, Elsinger H, Summer M, Thurner 4 S (2004) Network topology of the interbank market. Quant Finan 4(6):677–684CrossRefGoogle Scholar
  27. 27.
    Brummitt CD, Kobayashi T (2015) Cascades in multiplex financial networks with debts of different seniority. Phys Rev E 91(6):062813CrossRefGoogle Scholar
  28. 28.
    Brummitt CD, D’Souza RM, Leicht EA (2012) Suppressing cascades of load in interdependent networks. Proc Natl Acad Sci 109(12):E680–E689CrossRefGoogle Scholar
  29. 29.
    Buldyrev SV, Parshani R, Paul G, Stanley HE, Havlin S (2010) Catastrophic cascade of failures in interdependent networks. Nature 464(7291):1025–1028CrossRefGoogle Scholar
  30. 30.
    Buzna L, Peters K, Helbing D (2006) Modelling the dynamics of disaster spreading in networks. Physica A Stat Mech Appl 363(1):132–140CrossRefGoogle Scholar
  31. 31.
    Buzna L, Peters K, Ammoser H, Kühnert C, Helbing D (2007) Efficient response to cascading disaster spreading. Phys Rev E 75(5):056107CrossRefGoogle Scholar
  32. 32.
    Carreras BA, Newman DE, Gradney P, Lynch VE, Dobson I (2007) Interdependent risk in interacting infrastructure systems. In: 40th Annual Hawaii International Conference on System Sciences (HICSS 2007), pp 112–112. IEEE, Los AlamitosCrossRefGoogle Scholar
  33. 33.
    Cimini G, Squartini T, Garlaschelli D, Gabrielli A (2015) Systemic risk analysis on reconstructed economic and financial networks. Sci Rep 5:15758CrossRefGoogle Scholar
  34. 34.
    Coxeter HSM, Ball WWR (1960) Mathematical recreations essays. Macmillan, New YorkGoogle Scholar
  35. 35.
    Crucitti P, Latora V, Marchiori M (2004) A topological analysis of the Italian electric power grid. Physica A Stat Mech Appl 338(1–2):92–97CrossRefGoogle Scholar
  36. 36.
    Davis EP (1999) Financial data needs for macroprudential surveillance–what are the key indicators of risks to domestic financial stability? Lecture Series 2. Centre for Central Banking Studies, Bank of EnglandGoogle Scholar
  37. 37.
    De Domenico M, Solé-Ribalta A, Cozzo E, Kivelä M, Moreno Y, Porter MA, Gómez S, Arenas A (2013) Mathematical formulation of multilayer networks. Phys Rev X 3(4):041022Google Scholar
  38. 38.
    De Masi G, Iori G, Caldarelli G (2006) Fitness model for the Italian interbank money market. Phys Rev E 74(6):066112CrossRefGoogle Scholar
  39. 39.
    Del Vicario M, Bessi A, Zollo F, Petroni F, Scala A, Caldarelli G, Stanley HE, Quattrociocchi W (2016) The spreading of misinformation online. Proc Natl Acad Sci 113(3):554–559CrossRefGoogle Scholar
  40. 40.
    Delpini D, Battiston S, Riccaboni M, Gabbi G, Pammolli F, Caldarelli G (2013) Evolution of controllability in interbank networks. Sci Rep 3:1626CrossRefGoogle Scholar
  41. 41.
    Dong G, Gao J, Du R, Tian L, Stanley HE, Havlin S (2013) Robustness of network of networks under targeted attack. Phys Rev E 87(5):052804CrossRefGoogle Scholar
  42. 42.
    Dorogovtsev SN, Mendes JF (2013) Evolution of networks: from biological nets to the internet and WWW. Oxford University Press, OxfordzbMATHGoogle Scholar
  43. 43.
    Erdös P, Rényi A (1959) On random graphs, I. Publicationes Mathematicae (Debrecen) 6:290–297MathSciNetzbMATHGoogle Scholar
  44. 44.
    Esposito S, Stojadinovic B, Babič A, Dolšek M, Iqbal S, Selva J, Giardini D (2017) Engineering risk-based methodology for stress testing of critical non-nuclear infrastructures (strest project). In: Proceedings of 16th World Conference on Earthquake, 16WCEEGoogle Scholar
  45. 45.
    Estrada E (2012) The structure of complex networks: theory and applications. Oxford University Press, New YorkzbMATHGoogle Scholar
  46. 46.
    Faloutsos M, Faloutsos P, Faloutsos C (1999) On power-law relationships of the internet topology. In: ACM SIGCOMM Computer Communication Review, vol 29, pp 251–262. ACMzbMATHCrossRefGoogle Scholar
  47. 47.
    Galbusera L, Giannopoulos G (2018) On input-output economic models in disaster impact assessment. Int J Disaster Risk Reduct 30:186–198CrossRefGoogle Scholar
  48. 48.
    Galbusera L, Ward D, Giannopoulos G (2014) Developing stress tests to improve the resilience of critical infrastructures: a feasibility analysis. Technical Report, JRC Science and Policy Reports JRC91129, European CommissionGoogle Scholar
  49. 49.
    Galbusera L, Ward D, Giannopoulos G (2014) Stress tests and critical infrastructure protection-resilience. Technical Report, JRC Science and Policy Reports JRC93152, European CommissionGoogle Scholar
  50. 50.
    Galbusera L, Theodoridis G, Giannopoulos G (2015) Intelligent energy systems: introducing power–ICT interdependency in modeling and control design. IEEE Trans Ind Electron 62(4):2468–2477CrossRefGoogle Scholar
  51. 51.
    Gao J, Buldyrev SV, Havlin S, Stanley HE (2011) Robustness of a network of networks. Phys Rev Lett 107(19):195701CrossRefGoogle Scholar
  52. 52.
    Gao J, Buldyrev SV, Stanley HE, Havlin S (2012) Networks formed from interdependent networks. Nat Phys 8(1):40CrossRefGoogle Scholar
  53. 53.
    Gilbert EN (1959) Random graphs. Ann Math Stat 30(4):1141–1144zbMATHCrossRefGoogle Scholar
  54. 54.
    Giudicianni C, Di Nardo A, Di Natale M, Greco R, Santonastaso GF, Scala A (2018) Topological taxonomy of water distribution networks. Water 10(4):444CrossRefGoogle Scholar
  55. 55.
    Gudmundsson A, Mohajeri N (2013) Entropy and order in urban street networks. Sci Rep 3:3324CrossRefGoogle Scholar
  56. 56.
    Hałaj G, Kok C (2013) Assessing interbank contagion using simulated networks. Comput Manag Sci 10(2–3):157–186MathSciNetzbMATHCrossRefGoogle Scholar
  57. 57.
    Haldane AG, May RM (2011) Systemic risk in banking ecosystems. Nature 469(7330):351CrossRefGoogle Scholar
  58. 58.
    Helbing D (2012) Systemic risks in society and economics. In: Social self-organization, pp 261–284. Springer, Berlin/New YorkCrossRefGoogle Scholar
  59. 59.
    Helbing D (2013) Globally networked risks and how to respond. Nature 497(7447):51CrossRefGoogle Scholar
  60. 60.
    Iori G, De Masi G, Precup OV, Gabbi G, Caldarelli G (2008) A network analysis of the Italian overnight money market. J Econ Dyn Control 32(1):259–278zbMATHCrossRefGoogle Scholar
  61. 61.
    Jia T, Qin K, Shan J (2014) An exploratory analysis on the evolution of the us airport network. Physica A Stat Mech Appl 413:266–279CrossRefGoogle Scholar
  62. 62.
    Jonkeren O, Azzini I, Galbusera L, Ntalampiras S, Giannopoulos G (2015) Analysis of critical infrastructure network failure in the European union: a combined systems engineering and economic model. Netw Spat Econ 15(2):253–270MathSciNetzbMATHCrossRefGoogle Scholar
  63. 63.
    Kaluza P, Kölzsch A, Gastner MT, Blasius B (2010) The complex network of global cargo ship movements. J R Soc Interface 7(48):1093–1103CrossRefGoogle Scholar
  64. 64.
    Kim JY, Goh KI (2013) Coevolution and correlated multiplexity in multiplex networks. Phys Rev Lett 111(5):058702CrossRefGoogle Scholar
  65. 65.
    Kinney R, Crucitti P, Albert R, Latora V (2005) Modeling cascading failures in the north American power grid. Eur Phys J B Condens Matter Complex Syst 46(1):101–107CrossRefGoogle Scholar
  66. 66.
    Kivelä M, Arenas A, Barthelemy M, Gleeson JP, Moreno Y, Porter MA (2014) Multilayer networks. J Complex Netw 2(3):203–271CrossRefGoogle Scholar
  67. 67.
    Kok C, Montagna M (2016) Multi-layered interbank model for assessing systemic risk. Technical report, European Central BankGoogle Scholar
  68. 68.
    Korkali M, Veneman JG, Tivnan BF, Bagrow JP, Hines PD (2017) Reducing cascading failure risk by increasing infrastructure network interdependence. Sci Rep 7:44499CrossRefGoogle Scholar
  69. 69.
    Kotzanikolaou P, Theoharidou M, Gritzalis D (2013) Assessing n-order dependencies between critical infrastructures. Int J Crit Infrastruct 9(1–2):93–110CrossRefGoogle Scholar
  70. 70.
    Kotzanikolaou P, Theoharidou M, Gritzalis D (2013) Cascading effects of common-cause failures in critical infrastructures. In: International Conference on Critical Infrastructure Protection, pp 171–182. Springer, Washington, DCGoogle Scholar
  71. 71.
    Kühnert C, Helbing D, West GB (2006) Scaling laws in urban supply networks. Physica A Stat Mech Appl 363(1):96–103CrossRefGoogle Scholar
  72. 72.
    Latora V, Marchiori M (2002) Is the Boston subway a small-world network? Physica A Stat Mech Appl 314(1–4):109–113zbMATHCrossRefGoogle Scholar
  73. 73.
    Levy-Carciente S, Kenett DY, Avakian A, Stanley HE, Havlin S (2015) Dynamical macroprudential stress testing using network theory. J Bank Financ 59:164–181CrossRefGoogle Scholar
  74. 74.
    Li D, Zhang Q, Zio E, Havlin S, Kang R (2015) Network reliability analysis based on percolation theory. Reliab Eng Syst Saf 142:556–562CrossRefGoogle Scholar
  75. 75.
    Lin CT (1974) Structural controllability. IEEE Trans Autom Control 19(3):201–208MathSciNetzbMATHCrossRefGoogle Scholar
  76. 76.
    Lin Y, Patron A, Guo S, Kang R, Li D, Havlin S, Cohen R (2018) Design of survivable networks in the presence of aging. EPL (Europhysics Letters) 122(3):36003CrossRefGoogle Scholar
  77. 77.
    Liu YY, Barabási AL (2016) Control principles of complex systems. Rev Mod Phys 88(3):035006CrossRefGoogle Scholar
  78. 78.
    Liu YY, Slotine JJ, Barabási AL (2011) Controllability of complex networks. Nature 473(7346):167CrossRefGoogle Scholar
  79. 79.
    Liu YY, Slotine JJ, Barabási AL (2012) Control centrality and hierarchical structure in complex networks. PLoS One 7(9):e44459CrossRefGoogle Scholar
  80. 80.
    Louf R, Barthelemy M (2014) A typology of street patterns. J R Soc Interface 11(101):20140924CrossRefGoogle Scholar
  81. 81.
    Masucci AP, Stanilov K, Batty M (2013) Limited urban growth: London’s street network dynamics since the 18th century. PLoS One 8(8):e69469CrossRefGoogle Scholar
  82. 82.
    Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298(5594):824–827CrossRefGoogle Scholar
  83. 83.
    Morris RG, Barthelemy M (2013) Interdependent networks: the fragility of control. Sci Rep 3:2764CrossRefGoogle Scholar
  84. 84.
    Newman ME (2003) The structure and function of complex networks. SIAM Rev 45(2): 167–256MathSciNetzbMATHCrossRefGoogle Scholar
  85. 85.
    Newman M (2010) Networks: an introduction. Oxford University Press, OxfordzbMATHCrossRefGoogle Scholar
  86. 86.
    Nicosia V, Bianconi G, Latora V, Barthelemy M (2013) Growing multiplex networks. Phys Rev Lett 111(5):058701CrossRefGoogle Scholar
  87. 87.
    Nicosia V, Bianconi G, Latora V, Barthelemy M (2014) Nonlinear growth and condensation in multiplex networks. Phys Rev E 90(4):042807CrossRefGoogle Scholar
  88. 88.
    Ouyang M (2014) Review on modeling and simulation of interdependent critical infrastructure systems. Reliab Eng Syst Saf 121:43–60CrossRefGoogle Scholar
  89. 89.
    Ouyang M, Fei Q, Yu MH, Wang GX, Luan EJ (2009) Effects of redundant systems on controlling the disaster spreading in networks. Simul Model Pract Theory 17(2):390–397CrossRefGoogle Scholar
  90. 90.
    Pagani GA, Aiello M (2013) The power grid as a complex network: a survey. Physica A Stat Mech Appl 392(11):2688–2700MathSciNetzbMATHCrossRefGoogle Scholar
  91. 91.
    Parandehgheibi M, Modiano E (2013) Robustness of interdependent networks: the case of communication networks and the power grid. In: Global Communications Conference (GLOBECOM). IEEE, Piscataway, pp 2164–2169Google Scholar
  92. 92.
    Pastor-Satorras R, Vespignani A (2007) Evolution and structure of the internet: a statistical physics approach. Cambridge University Press, CambridgeGoogle Scholar
  93. 93.
    Pederson P, Dudenhoeffer D, Hartley S, Permann M (2006) Critical infrastructure interdependency modeling: a survey of us and international research. Idaho National Laboratory, pp 1–20Google Scholar
  94. 94.
    Petrone D, Latora V (2018) A dynamic approach merging network theory and credit risk techniques to assess systemic risk in financial networks. Sci Rep 8(1):5561CrossRefGoogle Scholar
  95. 95.
    Poledna S, Molina-Borboa JL, Martínez-Jaramillo S, Van Der Leij M, Thurner S (2015) The multi-layer network nature of systemic risk and its implications for the costs of financial crises. J Financ Stab 20:70–81CrossRefGoogle Scholar
  96. 96.
    Pósfai M, Gao J, Cornelius SP, Barabási AL, D’Souza RM (2016) Controllability of multiplex, multi-time-scale networks. Phys Rev E 94(3):032316CrossRefGoogle Scholar
  97. 97.
    Pu CL, Pei WJ, Michaelson A (2012) Robustness analysis of network controllability. Physica A Stat Mech Appl 391(18):4420–4425CrossRefGoogle Scholar
  98. 98.
    Quagliariello M (2009) Stress-testing the banking system: methodologies and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  99. 99.
    Rinaldi SM, Peerenboom JP, Kelly TK (2001) Identifying, understanding, and analyzing critical infrastructure interdependencies. IEEE Control Syst 21(6):11–25CrossRefGoogle Scholar
  100. 100.
    Rosato V, Bologna S, Tiriticco F (2007) Topological properties of high-voltage electrical transmission networks. Electr Power Syst Res 77(2):99–105CrossRefGoogle Scholar
  101. 101.
    Rosato V, Issacharoff L, Tiriticco F, Meloni S, Porcellinis S, Setola R (2008) Modelling interdependent infrastructures using interacting dynamical models. Int J Crit Infrastruct 4(1–2):63–79CrossRefGoogle Scholar
  102. 102.
    Rosato V, Meloni S, Simonsen I, Issacharoff L, Peters K, Von Festenberg N, Helbing D (2008) A complex system’s view of critical infrastructures. In: Helbing D (ed) Managing complexity: insights, concepts, applications, pp 241–260. Springer, BerlinCrossRefGoogle Scholar
  103. 103.
    Roukny T, Georg CP, Battiston S (2014) A network analysis of the evolution of the German interbank market. Technical report, Discussion Paper, Deutsche BundesbankGoogle Scholar
  104. 104.
    Samaniego H, Moses ME (2008) Cities as organisms: allometric scaling of urban road networks. J Transp Land Use 1(1):21–39Google Scholar
  105. 105.
    Santoro A, Latora V, Nicosia G, Nicosia V (2017) Pareto optimality in multilayer network growth. arXiv preprint: 1710.01068Google Scholar
  106. 106.
    Satumtira G, Dueñas-Osorio L (2010) Synthesis of modeling and simulation methods on critical infrastructure interdependencies research. In: Sustainable and resilient critical infrastructure systems, pp 1–51. Springer, Berlin/HeidelbergGoogle Scholar
  107. 107.
    Scellato S, Cardillo A, Latora V, Porta S (2006) The backbone of a city. Eur Phys J B Condens Matter Complex Syst 50(1–2):221–225CrossRefGoogle Scholar
  108. 108.
    Silva W, Kimura H, Sobreiro VA (2017) An analysis of the literature on systemic financial risk: a survey. J Financ Stab 28:91–114CrossRefGoogle Scholar
  109. 109.
    Son SW, Bizhani G, Christensen C, Grassberger P, Paczuski M (2012) Percolation theory on interdependent networks based on epidemic spreading. EPL (Europhysics Letters) 97(1):16006CrossRefGoogle Scholar
  110. 110.
    Soramäki K, Bech ML, Arnold J, Glass RJ, Beyeler WE (2007) The topology of interbank payment flows. Physica A Stat Mech Appl 379(1):317–333CrossRefGoogle Scholar
  111. 111.
    Stergiopoulos G, Kotzanikolaou P, Theocharidou M, Gritzalis D (2015) Risk mitigation strategies for critical infrastructures based on graph centrality analysis. Int J Crit Infrastruct Prot 10:34–44CrossRefGoogle Scholar
  112. 112.
    Strano E, Nicosia V, Latora V, Porta S, Barthélemy M (2012) Elementary processes governing the evolution of road networks. Sci Rep 2:296CrossRefGoogle Scholar
  113. 113.
    Strano E, Viana M, da Fontoura Costa L, Cardillo A, Porta S, Latora, V (2013) Urban street networks, a comparative analysis of ten European cities. Environ Plann B Plann Des 40(6):1071–1086CrossRefGoogle Scholar
  114. 114.
    Svendsen NK, Wolthusen SD (2007) Connectivity models of interdependency in mixed-type critical infrastructure networks. Inf Secur Tech Rep 12(1):44–55CrossRefGoogle Scholar
  115. 115.
    Theodoridis G, Galbusera L, Giannopoulos G (2015) Controllability assessment for cascade effects in ICT-enabled power grids. In: International Conference on Critical Information Infrastructures Security, pp 147–158. Springer, BerlinGoogle Scholar
  116. 116.
    Toroczkai Z, Vespignani A (2016) Understanding the fundamental principles underlying the survival and efficient recovery of multi-scale techno-social networks following a WMD event (a). Technical report, University of Notre Dame Du Lac Notre Dame United StatesCrossRefGoogle Scholar
  117. 117.
    Upper C, Worms A (2004) Estimating bilateral exposures in the German interbank market: is there a danger of contagion? Eur Econ Rev 48(4):827–849CrossRefGoogle Scholar
  118. 118.
    Čihák M (2004) Stress testing: a review of key concepts. Research and Policy Notes 2004/02, Czech National Bank, Research Department.
  119. 119.
    Vespignani A (2010) Complex networks: the fragility of interdependency. Nature 464(7291):984–985CrossRefGoogle Scholar
  120. 120.
    Vespignani A (2012) Modelling dynamical processes in complex socio-technical systems. Nat Phys 8(1):32CrossRefGoogle Scholar
  121. 121.
    Vespignani A (2018) Twenty years of network science. Nature 558:528–529CrossRefGoogle Scholar
  122. 122.
    Wandelt S, Sun X, Zhang J (2017) Evolution of domestic airport networks: a review and comparative analysis. Transportmetrica B Trans Dyn 13:1–17Google Scholar
  123. 123.
    Wang Z, Szolnoki A, Perc M (2014) Self-organization towards optimally interdependent networks by means of co evolution. New J Phys 16(3):033041CrossRefGoogle Scholar
  124. 124.
    Wang Z, Wang L, Szolnoki A, Perc M (2015) Evolutionary games on multilayer networks: a colloquium. Eur Phys J B 88(5):124CrossRefGoogle Scholar
  125. 125.
    Watts DJ, Strogatz SH (1998) Collective dynamics of “small-world” networks. Nature 393:440–442zbMATHCrossRefGoogle Scholar
  126. 126.
    West DB et al (2001) Introduction to graph theory, vol 2. Prentice Hall, Upper Saddle RiverGoogle Scholar
  127. 127.
    Yazdani A, Jeffrey P (2011) Complex network analysis of water distribution systems. Chaos Interdisciplinary J Nonlinear Sci 21(1):016111CrossRefGoogle Scholar
  128. 128.
    Zhang Y, Wang L, Sun W, Green II RC, Alam M (2011) Distributed intrusion detection system in a multi-layer network architecture of smart grids. IEEE Trans Smart Grid 2(4):796–808CrossRefGoogle Scholar
  129. 129.
    Zio E, Sansavini G (2011) Modeling interdependent network systems for identifying cascade-safe operating margins. IEEE Trans Reliab 60(1):94–101CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.European Commission, DG Joint Research Centre (JRC), Directorate E – Space, Security and MigrationTechnology Innovation in Security UnitIspraItaly

Personalised recommendations