Skip to main content
Log in

Complex Network Analysis of the Robustness of the Hanoi, Vietnam Bus Network

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

Many complex networks exist to facilitate the transport of material or information. In this capacity, the authors are often concerned with the continued flow of material or information when a fraction of the links in the complex network is disrupted. In other words, the authors are interested in the robustness of the complex network. In this paper, the authors survey measures of robustness like the average path length, the average clustering coefficient, the global efficiency, the size of largest cluster and use these to analyze the robustness of the bus network in Hanoi, Vietnam. The authors find that the bus network is robust against random failure but sensitive to targeted attack, in agreement with its scale-free character. By examining sharp drops in the average path length within the largest cluster of the Hanoi bus network under successive targeted attack, the authors identify five nodes whose loss lead to the fragmentation of the network into five or six disconnected clusters. These isolated clusters represent geographically the Central, Western, Southern, and Northwestern districts of Hanoi. Special considerations must therefore be given to these five nodes when planners wish to expand the bus network, or make it more robust.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chatterjee A and Ramadurai G, Scaling laws in Chennai bus network, Physics, arXiv: 1508.03504, 2015.

    Google Scholar 

  2. Chatterjee A, Manohar M, and Ramadurai G, Statistical analysis of bus networks in India, PloS one, 2016, 11(12): 1–16.

    Article  Google Scholar 

  3. Levinson H S, Zimmerman S, Clinger J, et al., Bus rapid transit: An overview, Journal of Public Transportation, 2002, 5(2): 1–30.

    Article  Google Scholar 

  4. Ceder A, Designing public transport networks and routes, Advanced Modeling for Transit Operations and Service Planning, 2002, 59–91.

    Chapter  Google Scholar 

  5. Ceder A and Wilson N H, Bus network design, Transportation Research Part B: Methodological, 1986, 20(4): 331–344.

    Article  Google Scholar 

  6. Vuchic V R, Urban Transit: Operations, Planning, and Economics, John Wiley and Sons, New Jersey, 2005.

    Google Scholar 

  7. Kocur G and Hendrickson C, Design of local bus service with demand equilibration, Transportation Science, 1982, 16(2): 149–170.

    Article  Google Scholar 

  8. Chang S K and Schonfeld P M, Multiple period optimization of bus transit systems, Transportation Research Part B: Methodological, 1991, 25(6): 453–478.

    Article  Google Scholar 

  9. Chien S I, Dimitrijevic B V, and Spasovic L N, Optimization of bus route planning in urban commuter networks, Journal of Public Transportation, 2003, 6(1): 53–79.

    Article  Google Scholar 

  10. Bielli M, Caramia M, and Carotenuto P, Genetic algorithms in bus network optimization, Transportation Research Part C: Emerging Technologies, 2002, 10(1): 19–34.

    Article  Google Scholar 

  11. Pattnaik S, Mohan S, and Tom V, Urban bus transit route network design using genetic algorithm, Journal of Transportation Engineering, 1998, 124(4): 368–375.

    Article  Google Scholar 

  12. Shrivastava P and O’Mahony M, A model for development of optimized feeder routes and coordinated schedules? A genetic algorithms approach, Transport Policy, 2006, 13(5): 413–425.

    Article  Google Scholar 

  13. Lin J and Ban Y, Complex network topology of transportation systems, Transport Reviews, 2013, 33(6): 658–685.

    Article  Google Scholar 

  14. de Regt R, von Ferber C, Holovatch Y, et al., Public transportation in UK viewed as a complex network, Physics and Society, arXiv: 1705.07266, 2017.

    Google Scholar 

  15. Sienkiewicz J and Holyst J A, Public transport systems in Poland: From Bialystok to Zielona Gora by bus and tram using universal statistics of complex networks, arXiv preprint physics/0503099, 2005, 1171–1178.

    Google Scholar 

  16. Sienkiewicz J and Holyst J A, Statistical analysis of 22 public transport networks in Poland, Physical Review E, 2005, 72(4): 1–11.

    Article  Google Scholar 

  17. Zhang H, Zhao P, Gao J, et al., The analysis of the properties of bus network topology in Beijing basing on complex networks, Mathematical Problems in Engineering, 2013, 2013: 1–6.

    Google Scholar 

  18. Lu H and Shi Y, Complexity of public transport networks, Tsinghua Science and Technology, 2007, 12(2): 204–213.

    Article  MATH  Google Scholar 

  19. Soh H, Lim S, Zhang T, et al., Weighted complex network analysis of travel routes on the Singapore public transportation system, Physica A: Statistical Mechanics and Its Applications, 2010, 389(24): 5852–5863.

    Article  Google Scholar 

  20. Von Ferber C, Holovatch Y, and Palchykov V, Scaling in public transport networks, arXiv preprint cond-mat/0501296, 2005.

    Book  Google Scholar 

  21. De Bona A, Fonseca K, Rosa M, et al., Analysis of public bus transportation of a brazilian city based on the theory of complex networks using the P-space, Mathematical Problems in Engineering, 2016, 2016: 1–12.

    Article  Google Scholar 

  22. Zhang H, Structural analysis of bus networks using indicators of graph theory and complex network theory, The Open Civil Engineering Journal, 2017, 11(1): 92–100.

    Article  Google Scholar 

  23. Trinh T T and Van Trinh C, Promoting public transport for sustainable urban development in Hanoi, Proceedings of the Eastern Asia Society for Transportation Studies, 2015, 10: 1–10.

    Google Scholar 

  24. Li K, Small M, Wang K, et al., Three structural properties reflecting the synchronizability of complex networks, Physical Review E, 2009, 79(6): 067201–067204.

    Article  MathSciNet  Google Scholar 

  25. Wang J, Hou X, Li K, et al., A novel weight neighborhood centrality algorithm for identifying influential spreaders in complex networks, Physica A: Statistical Mechanics and Its Applications, 2017, 475: 88–105.

    Article  Google Scholar 

  26. Cohen R and Havlin S, Complex Networks: Structure, Robustness and Function, Cambridge University Press, Cambridge, 2010.

    Book  MATH  Google Scholar 

  27. Boccaletti S, Latora V, Moreno Y, et al., Complex networks: Structure and dynamics, Physics reports, 2006, 424(4): 175–308.

    Article  MathSciNet  MATH  Google Scholar 

  28. Ellens W and Kooij R E, Graph measures and network robustness, arXiv: 1311.5064, 2013.

    Google Scholar 

  29. Albert R, Jeong H, and Barabasi A, Error and attack tolerance of complex networks, Nature, 2000, 406(6794): 378–832.

    Article  Google Scholar 

  30. Crucitti P, Latora V, Marchiori M, et al., Efficiency of scale-free networks: Error and attack tolerance, Physica A: Statistical Mechanics and Its Applications, 2003, 320: 622–642.

    Article  MATH  Google Scholar 

  31. Crucitti P, Latora V, Marchiori M, et al., Error and attack tolerance of complex networks, Physica A: Statistical Mechanics and Its Applications, 2004, 340(1): 388–394.

    Article  MathSciNet  MATH  Google Scholar 

  32. Broder A, Kumar R, Maghoul F, et al., Graph structure in the web, Computer Networks, 2000, 33(1): 309–320.

    Article  Google Scholar 

  33. Wang X F and Chen G, Complex networks: Small-world, scale-free and beyond, IEEE Circuits and Systems Magazine, 2003, 3(1): 6–20.

    Article  MathSciNet  Google Scholar 

  34. Jeong H, Tombor B, Albert R, et al., The large-scale organization of metabolic networks, Nature, 2000, 407(6804): 651–654.

    Article  Google Scholar 

  35. Sole R V and Montoya J M, Complexity and fragility in ecological networks, Proceedings Biological Sciences, 2001, 268(1480): 2039–2045.

    Article  Google Scholar 

  36. Sydney A, Scoglio C, Schumm P, et al., Elasticity: Topological characterization of robustness in complex networks, Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Sytems ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering), 2008.

    Google Scholar 

  37. Albert R and Barabasi A, Statistical mechanics of complex networks, Reviews of Modern Physics, 2002, 74(1): 47–101.

    Article  MathSciNet  MATH  Google Scholar 

  38. Latora V and Marchiori M, Is the Boston subway a small-world network?, Physica A: Statistical Mechanics and Its Applications, 2002, 314(1): 109–113.

    Article  MATH  Google Scholar 

  39. Latora V and Marchiori M, Efficient behavior of small-world networks, Physical Review Letters, 2001, 87(19): 198701.

    Article  Google Scholar 

  40. Blondel V D, Guillaume J, Lambiotte R, et al., Fast unfolding of communities in large networks, Journal of Statistical Mechanics: Theory and Experiment, 2008, 2008(10): 10008.

    Article  Google Scholar 

  41. Cohen R, Erez K, Ben-Avraham D, et al., Breakdown of the Internet under intentional attack, Physical Review Letters, 2001, 86(16): 3682–3685.

    Article  Google Scholar 

  42. Paul G, Tanizawa T, Havlin S, et al., Optimization of robustness of complex networks, The European Physical Journal B-Condensed Matter and Complex Systems, 2004, 38(2): 187–191.

    Article  Google Scholar 

  43. Zhang J, Xu X, Hong L, et al., Networked analysis of the Shanghai subway network, in China, Physica A: Statistical Mechanics and Its Applications, 2011, 390(23): 4562–4570.

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank BSc. Hoang Thanh Tung, Tomo app Vietnam, for bus network data collection.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ngoc Dung Bui.

Additional information

This paper was recommended for publication by Editor CHEN Jie.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tran, V.H., Cheong, S.A. & Bui, N.D. Complex Network Analysis of the Robustness of the Hanoi, Vietnam Bus Network. J Syst Sci Complex 32, 1251–1263 (2019). https://doi.org/10.1007/s11424-019-7431-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-019-7431-x

Keywords

Navigation