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Finding the n Most Vital Nodes in a Flow Network

Author

Listed:
  • H. W. Corley, Jr.

    (The University of Texas at Arlington)

  • Han Chang

    (The University of Texas at Arlington)

Abstract

The n most vital nodes in a network are those n nodes whose removal, along with all arcs incident with them, would cause the greatest decrease in maximum flow between a specified node pair. Results are established for this problem that lead to a procedure for determining the n most vital nodes.

Suggested Citation

  • H. W. Corley, Jr. & Han Chang, 1974. "Finding the n Most Vital Nodes in a Flow Network," Management Science, INFORMS, vol. 21(3), pages 362-364, November.
    • Handle: RePEc:inm:ormnsc:v:21:y:1974:i:3:p:362-364
    DOI: 10.1287/mnsc.21.3.362
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    Citations

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    Cited by:

    1. Alan Murray & Timothy Matisziw & Tony Grubesic, 2007. "Critical network infrastructure analysis: interdiction and system flow," Journal of Geographical Systems, Springer, vol. 9(2), pages 103-117, June.
    2. Samuel F Rosenblatt & Jeffrey A Smith & G Robin Gauthier & Laurent Hébert-Dufresne, 2020. "Immunization strategies in networks with missing data," PLOS Computational Biology, Public Library of Science, vol. 16(7), pages 1-21, July.
    3. Paola Cappanera & Maria Paola Scaparra, 2011. "Optimal Allocation of Protective Resources in Shortest-Path Networks," Transportation Science, INFORMS, vol. 45(1), pages 64-80, February.
    4. Xinyu Huang & Dongming Chen & Dongqi Wang & Tao Ren, 2020. "MINE: Identifying Top- k Vital Nodes in Complex Networks via Maximum Influential Neighbors Expansion," Mathematics, MDPI, vol. 8(9), pages 1-25, August.
    5. Ting Lei & Daoqin Tong, 2013. "Hedging against service disruptions: an expected median location problem with site-dependent failure probabilities," Journal of Geographical Systems, Springer, vol. 15(4), pages 491-512, October.
    6. Tony H. Grubesic & Timothy C. Matisziw & Alan T. Murray & Diane Snediker, 2008. "Comparative Approaches for Assessing Network Vulnerability," International Regional Science Review, , vol. 31(1), pages 88-112, January.
    7. M. Hosein Zare & Juan S. Borrero & Bo Zeng & Oleg A. Prokopyev, 2019. "A note on linearized reformulations for a class of bilevel linear integer problems," Annals of Operations Research, Springer, vol. 272(1), pages 99-117, January.
    8. Matthew Johnson & Alexander Gutfraind & Kiyan Ahmadizadeh, 2014. "Evader interdiction: algorithms, complexity and collateral damage," Annals of Operations Research, Springer, vol. 222(1), pages 341-359, November.
    9. Le Thi Khanh Hien & Melvyn Sim & Huan Xu, 2020. "Mitigating Interdiction Risk with Fortification," Operations Research, INFORMS, vol. 68(2), pages 348-362, March.
    10. Jabarzare, Ziba & Zolfagharinia, Hossein & Najafi, Mehdi, 2020. "Dynamic interdiction networks with applications in illicit supply chains," Omega, Elsevier, vol. 96(C).
    11. Shen, Yeming & Sharkey, Thomas C. & Szymanski, Boleslaw K. & Wallace, William (Al), 2021. "Interdicting interdependent contraband smuggling, money and money laundering networks," Socio-Economic Planning Sciences, Elsevier, vol. 78(C).
    12. Alice Paul & Susan E. Martonosi, 2024. "The all-pairs vitality-maximization (VIMAX) problem," Annals of Operations Research, Springer, vol. 338(2), pages 1019-1048, July.

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