Measuring the Topological Robustness of Transportation Networks to Disaster-Induced Failures: A Percolation Approach
Publication: Journal of Infrastructure Systems
Volume 26, Issue 2
Abstract
This paper presents a framework that integrates network theory methods into infrastructure network assessment in order to investigate transportation network robustness from a topological perspective. The objectives of this paper are threefold: (1) develop a framework that can effectively measure network performance under different stress levels (hazard scales); (2) determine the constraints of infrastructure networks’ spatially embedded nature in network robustness assessment; and (3) characterize the percolation transition in infrastructure networks and systematically evaluate cities’ robustness, and in doing so provide an evidence-driven evaluation framework for urban resilience planning. In this research, 13 city and 3 state transportation networks were investigated through both the proposed simulation and an analytical framework. The results show that (1) certain theoretical methods, such as generating functions, do not apply to transportation network analysis due to their unique spatially embedded features; (2) different city and state transportation networks’ degree distribution and percolation dynamics display similar patterns; (3) critical percolation threshold identifies the robustness feature in extreme cases and provides an early warning for urban traffic disruption, and the robustness index accurately measures the network robustness from a holistic point of view; and (4) reducing network spatial complexity by decreasing the node assortativity will make the empirical simulation comply with the theoretical results, which unveils the source of spatial essence inherent in infrastructure networks. Through the validation of different transportation networks, the proposed robustness assessment framework is verified to be able to extend the robustness analysis to a general network.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data used during the study are available online from OpenStreetMap (https://www.openstreetmap.org). The utilized Python module NetworkX is available online (https://networkx.github.io/).
Acknowledgments
The authors would like to acknowledge the funding support from the National Science Foundation through Grant CMMI No. 1563618. Any opinions, findings, and conclusion or recommendations expressed in this research are those of the authors and do not necessarily reflect the view of the funding agencies. The authors also would like to thank Mr. Cameron S. Bennett for his help with editing the language, which improved the readability and quality of this manuscript.
References
Abbar, S., T. Zanouda, and J. Borge-Holthoefer. 2016. “Robustness and resilience of cities around the world.” Preprint, submitted August 4, 2016. http://arxiv.org/abs/1608.01709.
Ahmed, R., M. Seedat, A. Van Niekerk, and S. Bulbulia. 2004. “Discerning community resilience in disadvantaged communities in the context of violence and injury prevention.” South African J. Psychol. 34 (3): 386–408. https://doi.org/10.1177/008124630403400304.
Albert, R., I. Albert, and G. L. Nakarado. 2004. “Structural vulnerability of the North American power grid.” Physical Review E 69 (2): 025103. https://doi.org/10.1103/PhysRevE.69.025103.
Albert, R., H. Jeong, and A.-L. Barabási. 1999. “Internet: Diameter of the world-wide web.” Nature 401 (6749): 130–131. https://doi.org/10.1038/43601.
Albert, R., H. Jeong, and A.-L. Barabási. 2000. “Error and attack tolerance of complex networks.” Nature 406 (6794): 378–382. https://doi.org/10.1038/35019019.
Arcaute, E., C. Molinero, E. Hatna, R. Murcio, C. Vargas-Ruiz, A. P. Masucci, and M. Batty. 2016. “Cities and regions in britain through hierarchical percolation.” R. Soc. Open Sci. 3 (4): 150691. https://doi.org/10.1098/rsos.150691.
Barabási, A.-L., and R. Albert. 1999. “Emergence of scaling in random networks.” Science 286 (5439): 509–512. https://doi.org/10.1126/science.286.5439.509.
Berche, B., C. von Ferber, T. Holovatch, and Y. Holovatch. 2010. “Public transport networks under random failure and directed attack.” Preprint, submitted February 11, 2010. http://arxiv.org/abs/1002.2300.
Berdica, K. 2002. “An introduction to road vulnerability: What has been done, is done and should be done.” Transport Policy 9 (2): 117–127. https://doi.org/10.1016/S0967-070X(02)00011-2.
Bird, J. F., and J. J. Bommer. 2004. “Earthquake losses due to ground failure.” Eng. Geol. 75 (2): 147–179. https://doi.org/10.1016/j.enggeo.2004.05.006.
Bruneau, M., S. E. Chang, R. T. Eguchi, G. C. Lee, T. D. O’Rourke, A. M. Reinhorn, M. Shinozuka, K. Tierney, W. A. Wallace, and D. von Winterfeldt. 2003. “A framework to quantitatively assess and enhance the seismic resilience of communities.” Earthquake Spectra 19 (4): 733–752. https://doi.org/10.1193/1.1623497.
Callaway, D. S., M. E. Newman, S. H. Strogatz, and D. J. Watts. 2000. “Network robustness and fragility: Percolation on random graphs.” Phys. Rev. Lett. 85 (25): 5468. https://doi.org/10.1103/PhysRevLett.85.5468.
Chang, S. E., and N. Nojima. 2001. “Measuring post-disaster transportation system performance: The 1995 Kobe earthquake in comparative perspective.” Transp. Res. Part A: Policy Pract. 35 (6): 475–494. https://doi.org/10.1016/S0965-8564(00)00003-3.
Cohen, R., K. Erez, D. Ben-Avraham, and S. Havlin. 2000. “Resilience of the internet to random breakdowns.” Phys. Rev. Lett. 85 (21): 4626. https://doi.org/10.1103/PhysRevLett.85.4626.
Cohen, R., K. Erez, D. Ben-Avraham, and S. Havlin. 2001. “Breakdown of the internet under intentional attack.” Phys. Rev. Lett. 86 (16): 3682. https://doi.org/10.1103/PhysRevLett.86.3682.
Crucitti, P., V. Latora, and M. Marchiori. 2004a. “A topological analysis of the Italian electric power grid.” Physica A 338 (1): 92–97. https://doi.org/10.1016/j.physa.2004.02.029.
Crucitti, P., V. Latora, M. Marchiori, and A. Rapisarda. 2004b. “Error and attack tolerance of complex networks.” Physica A 340 (1): 388–394. https://doi.org/10.1016/j.physa.2004.04.031.
Cuadra, L., S. Salcedo-Sanz, J. Del Ser, S. Jiménez-Fernández, and Z. W. Geem. 2015. “A critical review of robustness in power grids using complex networks concepts.” Energies 8 (9): 9211–9265. https://doi.org/10.3390/en8099211.
Dehghani, M. S., G. Flintsch, and S. McNeil. 2014. “Impact of road conditions and disruption uncertainties on network vulnerability.” J. Infrastruct. Syst. 20 (3): 04014015. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000205.
DeLaurentis, D., E.-P. Han, and T. Kotegawa. 2008. “Network-theoretic approach for analyzing connectivity in air transportation networks.” J. Aircr. 45 (5): 1669–1679. https://doi.org/10.2514/1.35244.
De Oliveira, E. L., L. Da Silva Portugal, and W. P. Junior. 2014. “Determining critical links in a road network: Vulnerability and congestion indicators.” Procedia-Soc. Behav. Sci. 162 (Dec): 158–167. https://doi.org/10.1016/j.sbspro.2014.12.196.
Dong, G., J. Gao, R. Du, L. Tian, H. E. Stanley, and S. Havlin. 2013. “Robustness of network of networks under targeted attack.” Phys. Rev. E 87 (5): 052804. https://doi.org/10.1103/PhysRevE.87.052804.
Dong, S., A. Esmalian, H. Farahmand, and A. Mostafavi. 2020a. “An integrated physical-social analysis of disrupted access to critical facilities and community service-loss tolerance in urban flooding.” Comput. Environ. Urban Syst. 80 (Mar): 101443. https://doi.org/10.1016/j.compenvurbsys.2019.101443.
Dong, S., A. Mostafizi, H. Wang, and P. Bosa. 2016. “Post-disaster mobility in disrupted transportation network: Case study of Portland, Oregon.” In Proc., 7th China-Japan-US Trilateral Symposium on Lifeline Earthquake Engineering. Reston, VA: ASCE.
Dong, S., H. Wang, A. Mostafavi, and J. Gao. 2019a. “Robust component: A robustness measure that incorporates access to critical facilities under disruptions.” J. R. Soc. Interface 16 (157): 20190149. https://doi.org/10.1098/rsif.2019.0149.
Dong, S., H. Wang, A. Mostafizi, and X. Song. 2020b. “A network-of-networks percolation analysis of cascading failures in spatially co-located road-sewer infrastructure networks.” Physica A 538: 122971. https://doi.org/10.1016/j.physa.2019.122971.
Dong, S., T. Yu, H. Farahmand, and A. Mostafavi. 2019b. “Bayesian modeling of flood control networks for failure cascade characterization and vulnerability assessment.” Comput.-Aided Civ. Infrastruct. Eng. 1–17.
Duan, Y., and F. Lu. 2013. “Structural robustness of city road networks based on community.” Comput. Environ. Urban Syst. 41 (Sep): 75–87. https://doi.org/10.1016/j.compenvurbsys.2013.03.002.
Duan, Y., and F. Lu. 2014. “Robustness of city road networks at different granularities.” Physica A 411 (Oct): 21–34. https://doi.org/10.1016/j.physa.2014.05.073.
Duch, J., and A. Arenas. 2007. “Effect of random failures on traffic in complex networks.” In Proc., 4th Int. Symp. on Fluctuations and Noise. Bellingham, WA: Society of Photo-Optical Instrumentation Engineers.
Dueñas-Osorio, L., J. I. Craig, B. J. Goodno, and A. Bostrom. 2007. “Interdependent response of networked systems.” J. Infrastruct. Syst. 13 (3): 185–194. https://doi.org/10.1061/(ASCE)1076-0342(2007)13:3(185).
Dunn, S., and S. M. Wilkinson. 2012. “Identifying critical components in infrastructure networks using network topology.” J. Infrastruct. Syst. 19 (2): 157–165. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000120.
Erdös, P., and A. Rényi. 1959. “On random graphs i.” Publ. Math. Debrecen 6 (18): 290–297.
Estrada, E. 2006. “Network robustness to targeted attacks. The interplay of expansibility and degree distribution.” Eur. Phys. J. B 52 (4): 563–574. https://doi.org/10.1140/epjb/e2006-00330-7.
Faloutsos, M., P. Faloutsos, and C. Faloutsos. 1999. “On power-law relationships of the internet topology.” In Vol. 29 of ACM SIGCOMM computer communication review, 251–262. New York: Association for Computing Machinery.
Galvan, G., and J. Agarwal. 2017. “Community detection in action: Identification of critical elements in infrastructure networks.” J. Infrastruct. Syst. 24 (1): 04017046. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000400.
Ganin, A. A., M. Kitsak, D. Marchese, J. M. Keisler, T. Seager, and I. Linkov. 2017. “Resilience and efficiency in transportation networks.” Sci. Adv. 3 (12): e1701079. https://doi.org/10.1126/sciadv.1701079.
Gao, J., B. Barzel, and A.-L. Barabási. 2016. “Universal resilience patterns in complex networks.” Nature 530 (7590): 307. https://doi.org/10.1038/nature16948.
Gao, J., S. V. Buldyrev, S. Havlin, and H. E. Stanley. 2011. “Robustness of a network of networks.” Phys. Rev. Lett. 107 (19): 195701. https://doi.org/10.1103/PhysRevLett.107.195701.
Gao, J., S. V. Buldyrev, H. E. Stanley, and S. Havlin. 2012. “Networks formed from interdependent networks.” Nat. Phys. 8 (1): 40–48. https://doi.org/10.1038/nphys2180.
Hagberg, A. A., D. A. Schult, and P. J. Swart. 2008. “Exploring network structure, dynamics, and function using NetworkX.” In Proc., 7th Python in Science Conf., 11–15. Oak Ridge, Tennessee: US Dept. of Energy Office of Scientific and Technical Information.
Holling, C. S. 1973. “Resilience and stability of ecological systems.” Annual Review of Ecology and Systematics 4 (1): 1–23. https://doi.org/10.1146/annurev.es.04.110173.000245.
Holme, P., B. J. Kim, C. N. Yoon, and S. K. Han. 2002. “Attack vulnerability of complex networks.” Phys. Rev. E 65 (5): 056109. https://doi.org/10.1103/PhysRevE.65.056109.
Holmgren, Å. J. 2006. “Using graph models to analyze the vulnerability of electric power networks.” Risk Anal. 26 (4): 955–969. https://doi.org/10.1111/j.1539-6924.2006.00791.x.
Hong, L., M. Ouyang, S. Peeta, X. He, and Y. Yan. 2015. “Vulnerability assessment and mitigation for the Chinese railway system under floods.” Reliab. Eng. Syst. Saf. 137 (May): 58–68. https://doi.org/10.1016/j.ress.2014.12.013.
Horner, M. W., and M. J. Widener. 2011. “The effects of transportation network failure on people’s accessibility to hurricane disaster relief goods: A modeling approach and application to a Florida case study.” Nat. Hazards 59 (3): 1619–1634. https://doi.org/10.1007/s11069-011-9855-z.
Huang, X., J. Gao, S. V. Buldyrev, S. Havlin, and H. E. Stanley. 2011. “Robustness of interdependent networks under targeted attack.” Phys. Rev. E 83 (6): 065101. https://doi.org/10.1103/PhysRevE.83.065101.
Iyer, S., T. Killingback, B. Sundaram, and Z. Wang. 2013. “Attack robustness and centrality of complex networks.” PLoS One 8 (4): e59613. https://doi.org/10.1371/journal.pone.0059613.
Jabareen, Y. 2013. “Planning the resilient city: Concepts and strategies for coping with climate change and environmental risk.” Cities 31 (Apr): 220–229. https://doi.org/10.1016/j.cities.2012.05.004.
Janić, M. 2015. “Modelling the resilience, friability and costs of an air transport network affected by a large-scale disruptive event.” Transp. Res. Part A: Policy Pract. 71 (Nov): 1–16.
Jenelius, E., T. Petersen, and L.-G. Mattsson. 2006. “Importance and exposure in road network vulnerability analysis.” Transp. Res. Part A: Policy Pract. 40 (7): 537–560.
Jeong, H., B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabási. 2000. “The large-scale organization of metabolic networks.” Nature 407 (6804): 651–654. https://doi.org/10.1038/35036627.
Keeley, J. E. 2005. “Fire history of the San Francisco East Bay region and implications for landscape patterns.” Int. J. Wildland Fire 14 (3): 285–296. https://doi.org/10.1071/WF05003.
Kermanshah, A., and S. Derrible. 2017. “Robustness of road systems to extreme flooding: Using elements of GIS, travel demand, and network science.” Nat. Hazards 86 (1): 151–164. https://doi.org/10.1007/s11069-016-2678-1.
Kinney, R., P. Crucitti, R. Albert, and V. Latora. 2005. “Modeling cascading failures in the North American power grid.” Eur. Phys. J. B 46 (1): 101–107. https://doi.org/10.1140/epjb/e2005-00237-9.
Kosmidis, K., S. Havlin, and A. Bunde. 2008. “Structural properties of spatially embedded networks.” Europhys. Lett. 82 (4): 48005. https://doi.org/10.1209/0295-5075/82/48005.
Kott, A., and T. Abdelzaher. 2014. “Resiliency and robustness of complex systems and networks.” Adapt. Dyn. Resilient Syst. 67 (Jun): 67–86.
Kurant, M., and P. Thiran. 2006. “Extraction and analysis of traffic and topologies of transportation networks.” Phys. Rev. E 74 (3): 036114. https://doi.org/10.1103/PhysRevE.74.036114.
LaRocca, S. 2014. “Modeling the reliability and robustness of critical infrastructure networks.” Ph.D. thesis, Dept. of Geography and Environmental Engineering, John Hopkins Univ.
LaRocca, S., J. Johansson, H. Hassel, and S. Guikema. 2015. “Topological performance measures as surrogates for physical flow models for risk and vulnerability analysis for electric power systems.” Risk Anal. 35 (4): 608–623. https://doi.org/10.1111/risa.12281.
Leskovec, J., and A. Krevl. 2014. SNAP Datasets: Stanford large network dataset collection (June). Accessed September 1, 2017. http://snap.stanford.edu/data.
Lhomme, S., D. Serre, Y. Diab, and R. Laganier. 2013. “Analyzing resilience of urban networks: A preliminary step towards more flood resilient cities.” Nat. Hazards Earth Syst. Sci. 13 (2): 221–230. https://doi.org/10.5194/nhess-13-221-2013.
Li, D., G. Li, K. Kosmidis, H. Stanley, A. Bunde, and S. Havlin. 2011. “Percolation of spatially constraint networks.” Europhys. Lett. 93 (6): 68004. https://doi.org/10.1209/0295-5075/93/68004.
Li, Q., S. Dong, and A. Mostafavi. 2019. “Modeling of inter-organizational coordination dynamics in resilience planning of infrastructure systems: A multilayer network simulation framework.” PLoS One 14 (11): 1–21.
Li, W., and X. Cai. 2004. “Statistical analysis of airport network of China.” Phys. Rev. E 69 (4): 046106. https://doi.org/10.1103/PhysRevE.69.046106.
Li, Y. 2014. “Assessing survivability of the Beijing subway system.” Int. J. Geospatial Environ. Res. 1 (1): 1–22.
Little, R. G. 2003. “Toward more robust infrastructure: Observations on improving the resilience and reliability of critical systems.” In Proc., 36th Annual Hawaii Int. Conf. on System Sciences. New York: IEEE.
Mapzen. 2017. “Mapzen.” Accessed July 1, 2017. https://mapzen.com/.
Mattsson, L.-G., and E. Jenelius. 2015. “Vulnerability and resilience of transport systems—A discussion of recent research.” Transp. Res. Part A: Policy Pract. 81 (Nov): 16–34.
McDaniels, T., S. Chang, D. Cole, J. Mikawoz, and H. Longstaff. 2008. “Fostering resilience to extreme events within infrastructure systems: Characterizing decision contexts for mitigation and adaptation.” Global Environ. Change 18 (2): 310–318. https://doi.org/10.1016/j.gloenvcha.2008.03.001.
Molloy, M., and B. Reed. 1998. “The size of the giant component of a random graph with a given degree sequence.” Comb. Probab. Comput. 7 (3): 295–305. https://doi.org/10.1017/S0963548398003526.
Moore, C., and M. E. Newman. 2000. “Exact solution of site and bond percolation on small-world networks.” Phys. Rev. E 62 (5): 7059. https://doi.org/10.1103/PhysRevE.62.7059.
Mostafizi, A., H. Wang, D. Cox, L. A. Cramer, and S. Dong. 2017. “Agent-based tsunami evacuation modeling of unplanned network disruptions for evidence-driven resource allocation and retrofitting strategies.” Nat. Hazards 88 (3): 1347–1372. https://doi.org/10.1007/s11069-017-2927-y.
Mostafizi, A., H. Wang, and S. Dong. 2019. “Understanding the multimodal evacuation behavior for a near-field tsunami.” Transp. Res. Rec. 2673 (11): 0361198119837511.
Motter, A. E., and Y.-C. Lai. 2002. “Cascade-based attacks on complex networks.” Phys. Rev. E 66 (6): 065102. https://doi.org/10.1103/PhysRevE.66.065102.
Murray-Tuite, P. M. 2006. “A comparison of transportation network resilience under simulated system optimum and user equilibrium conditions.” In Proc., 38th Conf. on Winter Simulation, 1398–1405. New York: IEEE.
Nas, U. 2012. “Disaster resilience: A national imperative.” Environ.: Sci. Policy Sustainable Develop. 55 (2): 25–29. https://doi.org/10.1080/00139157.2013.768076.
Newman, M. 2010. Networks: An introduction. Oxford, UK: Oxford University Press.
Newman, M. E. 2002. “Assortative mixing in networks.” Phys. Rev. Lett. 89 (20): 208701. https://doi.org/10.1103/PhysRevLett.89.208701.
Newman, M. E. 2003. “Mixing patterns in networks.” Phys. Rev. E 67 (2): 026126. https://doi.org/10.1103/PhysRevE.67.026126.
Nourzad, S. H. H., and A. Pradhan. 2015. “Vulnerability of infrastructure systems: Macroscopic analysis of critical disruptions on road networks.” J. Infrastruct. Syst. 22 (1): 04015014. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000266.
Oregon Live, T. O. n.d. “PGE reports about 9,000 customers without power.” Accessed April 1, 2018. https://www.oregonlive.com/portland/index.ssf/2017/01/pgereports33kcustomerswith:html.
O’Rourke, T. D. 2007. “Critical infrastructure, interdependencies, and resilience.” BRIDGE-Washington-Nat. Acad. Eng. 37 (1): 22.
Peduzzi, P. 2004. “Is climate change increasing the frequency of hazardous events.” Accessed September 1, 2017. https://commons.wikimedia.org/wiki/File%3ATrends_in_natural_disasters.jpg.
Pepyne, D. L. 2007. “Topology and cascading line outages in power grids.” J. Syst. Sci. Syst. Eng. 16 (2): 202–221. https://doi.org/10.1007/s11518-007-5044-8.
Reggiani, A. 2013. “Network resilience for transport security: Some methodological considerations.” Transport Policy 28: 63–68. https://doi.org/10.1016/j.tranpol.2012.09.007.
Rockefeller Foundation. 2019. 100 Resilient Cities Initiative. Accessed July 31, 2019. https://www.100resilientcities.org/.
Rosas-Casals, M., S. Valverde, and R. V. Solé. 2007. “Topological vulnerability of the European power grid under errors and attacks.” Int. J. Bifurcation Chaos 17 (7): 2465–2475. https://doi.org/10.1142/S0218127407018531.
Sakakibara, H., Y. Kajitani, and N. Okada. 2004. “Road network robustness for avoiding functional isolation in disasters.” J. Transp. Eng. 130 (5): 560–567. https://doi.org/10.1061/(ASCE)0733-947X(2004)130:5(560).
Schneider, C. M., A. A. Moreira, J. S. Andrade, S. Havlin, and H. J. Herrmann. 2011. “Mitigation of malicious attacks on networks.” Proc. Nat. Acad. Sci. 108 (10): 3838–3841. https://doi.org/10.1073/pnas.1009440108.
Scott, D. M., D. C. Novak, L. Aultman-Hall, and F. Guo. 2006. “Network robustness index: A new method for identifying critical links and evaluating the performance of transportation networks.” J. Transp. Geogr. 14 (3): 215–227. https://doi.org/10.1016/j.jtrangeo.2005.10.003.
Sen, C. 2014. “How 2 inches of snow created a traffic nightmare in Atlanta.” Accessed August 1, 2017. https://www.theatlantic.com/business/archive/2014/01/how-2-inches-of-snow-created-a-traffic-nightmare-in-atlanta/283434/.
Shoji, G., and A. Toyota. 2009. “Modeling of restoration process associated with critical infrastructure and its interdependency due to a seismic disaster.” In Proc., TCLEE 2009: Lifeline Earthquake Engineering in a Multihazard Environment 1–12. Reston, VA: ASCE.
Simonoff, J., C. Restrepo, R. Zimmerman, and Z. Naphtali. 2007. “Analysis of electrical power and oil and gas pipeline failures.” In Proc., Int. Conf. on Critical Infrastructure Protection, 381–394. Berlin: Springer.
Simonsen, I., L. Buzna, K. Peters, S. Bornholdt, and D. Helbing. 2008. “Transient dynamics increasing network vulnerability to cascading failures.” Phys. Rev. Lett. 100 (21): 218701. https://doi.org/10.1103/PhysRevLett.100.218701.
Sullivan, J., D. Novak, L. Aultman-Hall, and D. M. Scott. 2010. “Identifying critical road segments and measuring system-wide robustness in transportation networks with isolating links: A link-based capacity-reduction approach.” Transp. Res. Part A: Policy Pract. 44 (5): 323–336.
Sun, P., X.-B. Cao, W.-B. Du, and C.-L. Chen. 2010. “The effect of geographical distance on epidemic spreading.” Phys. Procedia 3 (5): 1811–1818. https://doi.org/10.1016/j.phpro.2010.07.023.
Tamima, U., and L. Chouinard. 2017. “Systemic seismic vulnerability of transportation networks and emergency facilities.” J. Infrastruct. Syst. 23 (4): 04017032. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000392.
Taylor, M. A. 2008. “Critical transport infrastructure in urban areas: Impacts of traffic incidents assessed using accessibility-based network vulnerability analysis.” Growth Change 39 (4): 593–616. https://doi.org/10.1111/j.1468-2257.2008.00448.x.
Thedchanamoorthy, G., M. Piraveenan, D. Kasthuriratna, and U. Senanayake. 2014. “Node assortativity in complex networks: An alternative approach.” Procedia Comput. Sci. 29: 2449–2461. https://doi.org/10.1016/j.procs.2014.05.229.
Van Mieghem, P., C. Doerr, H. Wang, J. M. Hernandez, D. Hutchison, M. Karaliopoulos, and R. Kooij. 2010. A framework for computing topological network robustness. Delft, Netherlands: Delft Univ. of Technology.
Vespignani, A. 2010. “Complex networks: The fragility of interdependency.” Nature 464 (7291): 984–985. https://doi.org/10.1038/464984a.
Wang, W., S. Yang, H. E. Stanley, and J. Gao. 2019. “Local floods induce large-scale abrupt failures of road networks.” Nat. Commun. 10 (1): 2114. https://doi.org/10.1038/s41467-019-10063-w.
Wang, X. F., and G. Chen. 2003. “Complex networks: Small-world, scale-free and beyond.” IEEE Circuits Syst. Mag. 3 (1): 6–20. https://doi.org/10.1109/MCAS.2003.1228503.
Wang, Z., A. P. Chan, J. Yuan, B. Xia, M. Skitmore, and Q. Li. 2014. “Recent advances in modeling the vulnerability of transportation networks.” J. Infrastruct. Syst. 21 (2): 06014002. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000232.
Wilf, H. S. 2013. Generating functionology. Amsterdam, Netherlands: Elsevier.
Willis, H. H., A. R. Morral, T. K. Kelly, and J. J. Medby. 2006. Estimating terrorism risk. Santa Monica, CA: Rand Corporation.
Winkler, J., L. Duenas-Osorio, R. Stein, and D. Subramanian. 2010. “Performance assessment of topologically diverse power systems subjected to hurricane events.” Reliab. Eng. Syst. Saf. 95 (4): 323–336. https://doi.org/10.1016/j.ress.2009.11.002.
Worldwatch-Institute. 2016. Can a city be sustainable? State of the world. Washington, DC: Island Press.
Yazdani, A., and P. Jeffrey. 2010. “A complex network approach to robustness and vulnerability of spatially organized water distribution networks.” Preprint, submitted August 10, 2010. http://arxiv.org/abs/1008.1770.
Zhang, P., B. Cheng, Z. Zhao, D. Li, G. Lu, Y. Wang, and J. Xiao. 2013. “The robustness of interdependent transportation networks under targeted attack.” Europhys. Lett. 103 (6): 68005. https://doi.org/10.1209/0295-5075/103/68005.
Information & Authors
Information
Published In
Journal of Infrastructure Systems
Volume 26 • Issue 2 • June 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: May 9, 2018
Accepted: Oct 1, 2019
Published online: Mar 5, 2020
Published in print: Jun 1, 2020
Discussion open until: Aug 5, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.