Integration of stress testing with graph theory to assess the resilience of urban road networks under seismic hazards


Transportation networks daily provide accessibility and crucial services to societies. However, they must also maintain an acceptable level of service to critical infrastructures in the case of disruptions, especially during natural disasters. We have developed a method for assessing the resilience of transportation network topology when exposed to environmental hazards. This approach integrates graph theory with stress testing methodology and involves five basic steps: (1) establishment of a scenario set that covers a range of seismic damage potential in the network, (2) assessment of resilience using various graph-based metrics, (3) topology-based simulations, (4) evaluation of changes in graph-based metrics, and (5) examination of resilience in terms of spatial distribution of critical nodes and the entire network topology. Our case study was from the city of Kathmandu in Nepal, where the earthquake on April 25, 2015, followed by a major aftershock on May 12, 2015, led to numerous casualties and caused significant damage. Therefore, it is a good example for demonstrating and validating the developed methodology. The results presented here indicate that the proposed approach is quite efficient and accurate in assisting stakeholders when evaluating the resilience of transportation networks based on their topology.

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\(B_{{x,{\text{before}}}}\) :

Betweenness value of node x before disruption

\(B_{{x,{\text{after}}}}\) :

Betweenness value of same node x after disruption

\({\text{Diff}}_{x}\) :

Difference in node importance metric

\(d_{ij}\) :

Network distance between nodes i and j


Giant connected component

\(\hat{K}\) :

Kappa coefficient

n :

Total number of nodes

\(N_{{{\text{GCC, after}}}}\) :

Normalized GCC after disruption

\(N_{{{\text{GCC, before}}}}\) :

Normalized GCC before disruption

\(N_{{{\text{eff, hypothetical}}}}\) :

Network efficiency for hypothetical networks

\(N_{{{\text{eff, network}}}}\) :

Network efficiency for study area

\(N_{{{\text{GCC, hypothetical}}}}\) :

Network robustness for hypothetical networks

\(N_{{{\text{GCC, network}}}}\) :

Network robustness for study area

\(n_{ij}\) :

Total number of shortest paths between nodes i and j

\(n_{ij} \left( x \right)\) :

Number of times node x is used while traveling through network

p :

Probability of node removal

\(r\) :

Number of rows in error matrix

\({\text{RES}}_{{{\text{S1, eff}}}}\) :

Resilience of study area in terms of network efficiency

\({\text{RES}}_{{{\text{S1, GCC}}}}\) :

Resilience of study area in terms of network robustness

s :

Sample size

\(S1\) :

Scenario 1


Stress testing

\(x_{i + } ,x_{ + i}\) :

Marginal totals for row \(i\)

\(x_{ii}\) :

Total number of observations in row \(i\) and column \(i\)


  1. Ainuddin S, Routray JK (2012) Earthquake hazards and community resilience in Baluchistan. Nat Hazards 63(2):909–937.

    Article  Google Scholar 

  2. Albert R, Jeong H, Barabasi A-L (2000) Error and attack tolerance of complex networks. Nature 406:378–382

    Article  Google Scholar 

  3. Avdeeva Y, van Gelder P (2014) Infrarisk Deliverable D6.1 Stress test methodologies. European Commission

  4. Bíl M, Vodák R, Kubeček J, Bílová M, Sedoník J (2015) Evaluating road network damage caused by natural disasters in the Czech Republic between 1997 and 2010. Transp Res Part A Policy Pract 80:90–103.

    Article  Google Scholar 

  5. Bono F, Gutiérrez E (2011) A network-based analysis of the impact of structural damage on urban accessibility following a disaster: the case of the seismically damaged Port Au Prince and Carrefour urban road networks. J Transp Geogr 19(6):1443–1455.

    Article  Google Scholar 

  6. Bruneau M, Chang SE, Eguchi RT, Lee GC, O’Rourke TD, Reinhorn AM, Shinozuka M, Tierney K, Wallace WA, von Winterfeldt D (2003) A framework to quantitatively assess and enhance the seismic resilience of communities. Earthq Spectra 19(4):733–752.

    Article  Google Scholar 

  7. Çetinkaya EK, Broyles D, Dandekar A, Srinivasan S, Sterbenz JP (2013) Modelling communication network challenges for Future Internet resilience, survivability, and disruption tolerance: a simulation-based approach. Telecommun Syst 52(2):751–766

    Google Scholar 

  8. Çetinkaya EK, Alenazi MJF, Peck AM, Rohrer JP, Sterbenz JPG (2015) Multilevel resilience analysis of transportation and communication networks. Telecommun Syst 60(4):515–537.

    Article  Google Scholar 

  9. Cimellaro GP, Reinhorn AM, Bruneau M (2010) Framework for analytical quantification of disaster resilience. Eng Struct 32(11):3639–3649.

    Article  Google Scholar 

  10. Clarke J, O’Brien E (2016) A multi-hazard risk assessment methodology, stress test framework and decision support tool for resilient critical infrastructure. In: Proceedings of 6th transport research conference moving forward: innovative solutions for tomorrow’s mobility, Warsaw, Poland, 18–21 April 2016

  11. Cohen J (1960) A coefficient of agreement for nominal scales. Educ Psychol Meas 20:37–46

    Article  Google Scholar 

  12. Congalton RG (1991) A review of assessing the accuracy of classifications of remotely sensed data. Remote Sens Environ 37:35–46

    Article  Google Scholar 

  13. Cumming GS (2011) Spatial resilience in networks. In: Cumming GS (ed) Spatial resilience in social-ecological systems. Springer, Dordrecht, pp 121–142.

    Google Scholar 

  14. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1:269–271

    Article  Google Scholar 

  15. Dorbritz R (2011) Assessing the resilience of transportation systems in case of large-scale disastrous events. In: Proceedings of the 8th international conference on environmental engineering, Vilnius Lithuania, pp 1070–1076

  16. Dorbritz R, Weidmann U (2009) Stability of public transportation systems in case of random failures and intended attacks—a case study from Switzerland. In: Systems Safety 2009. In: Incorporating the SaRS annual conference, 4th IET international conference, London, UK, pp 1–6

  17. Ellens W, Kooij RE (2013) Graph measures and network robustness. http://arxivorg/abs/13115064v1

  18. ESRI (2017) Classification methods. Accessed 14 Aug 2017

  19. European Commission (2012) Communication from the commission to the council and the European Parliament on the comprehensive risk and safety assessments (“stress tests”) of nuclear power plants in the European Union and related activities. European Commission, Brussels

    Google Scholar 

  20. Eusgeld I, Kröger W, Sansavini G, Schläpfer M, Zio E (2009) The role of network theory and object-oriented modeling within a framework for the vulnerability analysis of critical infrastructures. Reliab Eng Syst Saf 94(5):954–963.

    Article  Google Scholar 

  21. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41

    Article  Google Scholar 

  22. Freeman LC (1979) Centrality in social networks: conceptual clarification. Soc Netw 1:215–239

    Article  Google Scholar 

  23. Freiria S, Ribeiro B, Tavares AO (2015) Understanding road network dynamics: link-based topological patterns. J Transp Geogr 46:55–66.

    Article  Google Scholar 

  24. Garousi V (2010) A genetic algorithm-based stress test requirements generator tool and its empirical evaluation. IEEE Trans Softw Eng 36(6):778–797.

    Article  Google Scholar 

  25. Garschagen M (2011) Resilience and organisational institutionalism from a cross-cultural perspective: an exploration based on urban climate change adaptation in Vietnam. Nat Hazards 67(1):25–46.

    Article  Google Scholar 

  26. Gastner MT, Newman MEJ (2006) The spatial structure of networks. Eur Phys J 49:247–252.

    Article  Google Scholar 

  27. Grubesic TH, Matisziw TC, Murray AT, Snediker D (2008) Comparative approaches for assessing network vulnerability. Int Reg Sci Rev 31(1):88–112.

    Article  Google Scholar 

  28. Homeland Security Studies & Analysis Institute (2009) Concept development: an operational framework for resilience

  29. Huges JF, Healy K (2014) Measuring the resilience of transport infrastructure. NZ Transport Agency, New Zealand

    Google Scholar 

  30. Hutter G, Kuhlicke C, Glade T, Felgentreff C (2013) Natural hazards and resilience: exploring institutional and organizational dimensions of social resilience. Nat Hazards 67:1–6

    Article  Google Scholar 

  31. igraph (2017) The network analysis package. Accessed 16 March 2017

  32. Immers B, Bleukx A, Stada J, Tampere C, Yperman I (2004) Robustness and resilience of road network structures. In: NECTAR cluster meeting on reliability of networks, Amsterdam, Netherlands

  33. Janssen LLF, Wel F (1994) Accuracy assessment of satellite derived land cover data: a review. IEEE Photogramm Eng Remote Sens 60:419–426

    Google Scholar 

  34. Jenelius E, Mattsson L-G (2015) Road network vulnerability analysis: conceptualization, implementation and application. Comput Environ Urban Syst 49:136–147.

    Article  Google Scholar 

  35. Klein RJT, Nicholls RJ, Thomalla F (2003) Resilience to natural hazards: how useful is this concept? Environ Hazards 5(1):35–45.

    Article  Google Scholar 

  36. Lama PD, Becker P, Bergström J (2017) Scrutinizing the relationship between adaptation and resilience: longitudinal comparative case studies across shocks in two Nepalese villages. Int J Disaster Risk Reduct.

    Google Scholar 

  37. Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 87(19):198701.

    Article  Google Scholar 

  38. Latora V, Marchiori M (2005) Vulnerability and protection of infrastructure networks. Phys Rev E: Stat, Nonlin, Soft Matter Phys 71(1 Pt 2):015103.

    Article  Google Scholar 

  39. Lu Z, Im J, Rhee J, Hodgson M (2014) Building type classification using spatial and landscape attributes derived from LiDAR remote sensing data. Landsc Urban Plan 130:134–148.

    Article  Google Scholar 

  40. Marra WA, Kleinhans MG, Addink EA (2014) Network concepts to describe channel importance and change in multichannel systems: test results for the Jamuna River, Bangladesh. Earth Surf Process Landf 39(6):766–778.

    Article  Google Scholar 

  41. Meier JD, Farre C, Bansode P, Barber S, Rea D (2007) Chapter 18—stress testing web applications

  42. Mishra A, Ghate R, Maharjan A, Gurung J, Pathak G, Upraity AN (2017) Building ex ante resilience of disaster-exposed mountain communities: drawing insights from the Nepal earthquake recovery. Int J Disaster Risk Reduct 22:167–178.

    Article  Google Scholar 

  43. Murray-Tuite PM (2006) A comparison of transportation network resilience under simulated system optimum and user equilibrium conditions. In: Proceedings of the 38th winter simulation conference, Monterey, CA, pp 1398–1405

  44. Newman MEJ (2010) Networks: an introduction. Oxford University Press, Oxford

    Google Scholar 

  45. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113

    Article  Google Scholar 

  46. Office of Superintendent of Financial Institutions of Canada (2009) Stress Testing Guideline, Canada

  47. Okabe A, Yamada I (2001) The K-function method on a network and its computational implementation. Geogr Anal 33(3):271–290

    Article  Google Scholar 

  48. Okabe A, Okunuki K, Shiode S (2006) SANET: a toolbox for spatial analysis on a network. Geogr Anal 38(1):57–66.

    Article  Google Scholar 

  49. Okabe A, Satoh T, Sugihara K (2009) A kernel density estimation method for networks, its computational method and a GIS-based tool. Int J Geogr Inf Sci 23(1):7–32.

    Article  Google Scholar 

  50. Onder S, Damar B, Hekimoglu AA (2016) Macro stress testing and an application on Turkish banking sector1. Proc Econ Finance 38:17–37.

    Article  Google Scholar 

  51. Park J, Seager TP, Rao PS (2011) Lessons in risk- versus resilience-based design and management. Integr Environ Assess Manag 7(3):396–399.

    Article  Google Scholar 

  52. Parsons M, Glavac S, Hastings P, Marshall G, McGregor J, McNeill J, Morley P, Reeve I, Stayner R (2016) Top-down assessment of disaster resilience: a conceptual framework using coping and adaptive capacities. Int J Disaster Risk Reduct 19:1–11.

    Article  Google Scholar 

  53. Pitilakis K, Argyroudis S, Kakderi K, Selva J (2016) Systemic vulnerability and risk assessment of transportation systems under natural hazards towards more resilient and robust infrastructures. Transp Res Proc 14:1335–1344.

    Article  Google Scholar 

  54. Porta S, Crucitti P, Latora V (2006) The network analysis of Urban Streets: a primal approach. Environ Plann B Plann Design 33(5):705–725.

    Article  Google Scholar 

  55. Schintler LA, Gorman S, Kulkarni R, Stough R (2007a) 14 moving from protection to resiliency: a path to securing critical infrastructure. In: Murray AT, Grubesic T (eds) Critical infrastructure reliability and vulnerability. Springer, Leipzig, pp 291–307

    Google Scholar 

  56. Schintler LA, Kulkarni R, Gorman S, Stough R (2007b) Using raster-based GIS and graph theory to analyze complex networks. Netw Spat Econ 7(4):301–313.

    Article  Google Scholar 

  57. Shakya M, Kawan CK (2016) Reconnaissance based damage survey of buildings in Kathmandu valley: an aftermath of 7.8 Mw, 25 April 2015 Gorkha (Nepal) earthquake. Eng Fail Anal 59:161–184.

    Article  Google Scholar 

  58. Sinha P, Kumar L, Drielsma M, Barrett T (2014) Time-series effective habitat area (EHA) modeling using cost-benefit raster based technique. Ecol Inform 19:16–25.

    Article  Google Scholar 

  59. Strano E, Nicosia V, Latora V, Porta S, Barthelemy M (2012) Elementary processes governing the evolution of road networks. Sci Rep 2:296.

    Article  Google Scholar 

  60. STREST (2017) Harmonized approach to stress tests for critical infrastructures against natural hazards. European Commission. Accessed 16 Aug 2017

  61. United Nations (2015) Sendai framework for disaster risk reduction 2015–2030, Sendai, Japan

  62. United Nations Office for Disaster Risk Reduction (2007) Terminology. Accessed 1 Aug 2016

  63. Vragovi I, Louis E, Díaz-Guilera A (2005) Efficiency of informational transfer in regular and complex networks. Phys Rev E 71:036122.

    Article  Google Scholar 

  64. Worldbank (2013) Managing Nepal’s Urban Transition. Accessed 1 Aug 2016

  65. Xie Z, Yan J (2008) Kernel density estimation of traffic accidents in a network space. Comput Environ Urban Syst 32(5):396–406.

    Article  Google Scholar 

  66. Xue F, Lin L, Ti W, Lu N (2007) Vibration assessment method and engineering applications to small bore piping in nuclear power plant. In: Proceedings of nuclear power plant life management, Shanghai, China, vol 48

  67. Yang Y, Liu Y, Zhou M, Li F, Sun C (2015) Robustness assessment of urban rail transit based on complex network theory: a case study of the Beijing Subway. Saf Sci 79:149–162.

    Article  Google Scholar 

  68. Zhang X, Miller-Hooks E, Denny K (2015) Assessing the role of network topology in transportation network resilience. J Transp Geogr 46:35–45.

    Article  Google Scholar 

  69. Zhou H, Ja Wang, Wan J, Jia H (2009) Resilience to natural hazards: a geographic perspective. NatHazards 53(1):21–41.

    Article  Google Scholar 

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This work was funded by a grant to N.Y.A. and H.R.H. from the National Research Foundation of Singapore (NRF) under its Campus for Research Excellence and Technological Enterprise (CREATE) program (FI 370074011) for the Future Resilient Systems project at the Singapore-ETH Centre (SEC) and by an Alexander von Humboldt Foundation Georg Forster Experienced Researcher Fellowship Grant to H.S.D., hosted by F.W.

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Correspondence to Nazli Yonca Aydin.

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Aydin, N.Y., Duzgun, H.S., Wenzel, F. et al. Integration of stress testing with graph theory to assess the resilience of urban road networks under seismic hazards. Nat Hazards 91, 37–68 (2018).

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  • Disaster resilience
  • Earthquake
  • Graph theory
  • Resilience assessment
  • Stress testing
  • Transportation infrastructure
  • Road network
  • Resilience