Natural Hazards

, Volume 91, Issue 1, pp 37–68 | Cite as

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

  • Nazli Yonca AydinEmail author
  • H. Sebnem Duzgun
  • Friedemann Wenzel
  • Hans Rudolf Heinimann
Original Paper


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.


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

List of symbols


Betweenness value of node x before disruption


Betweenness value of same node x after disruption


Difference in node importance metric


Network distance between nodes i and j


Giant connected component


Kappa coefficient


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


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


Probability of node removal


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


Sample size


Scenario 1


Stress testing

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

Marginal totals for row \(i\)


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



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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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Future Resilient Systems at Singapore-ETH CentreETH ZurichSingaporeSingapore
  2. 2.Colorado School of MinesDepartment of Mining EngineeringGoldenUSA
  3. 3.Karlsruhe Institute of Technology, Geophysical InstituteKarlsruheGermany

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