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Finding Critical Links for Closeness Centrality

Author

Listed:
  • Alexander Veremyev

    (Industrial Engineering and Management Systems, University of Central Florida, Orlando, Florida 32816)

  • Oleg A. Prokopyev

    (Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261)

  • Eduardo L. Pasiliao

    (Munitions Directorate, Air Force Research Laboratory, Eglin AFB, Florida 32542)

Abstract

Closeness centrality is a class of distance-based measures in the network analysis literature to quantify reachability of a given vertex (or a group of vertices) by other network agents. In this paper, we consider a new class of critical edge detection problems, in which given a group of vertices that represent an important subset of network elements of interest (e.g., servers that provide an essential service to the network), the decision maker is interested in identifying a subset of critical edges whose removal maximally degrades the closeness centrality of those vertices. We develop a general optimization framework, in which the closeness centrality measure can be based on any nonincreasing function of distances between vertices, which, in turn, can be interpreted as communication efficiency between them. Our approach includes three well-known closeness centrality measures as special cases: harmonic centrality , decay centrality , and k -step reach centrality . Furthermore, for quantifying the centrality of a group of vertices we consider three different approaches for measuring the reachability of the group from any vertex in the network: minimum distance to a vertex in the group, maximum distance to a vertex in the group, and the average centrality of vertices in the group. We study the theoretical computational complexity of the proposed models and describe the corresponding mixed integer programming formulations. For solving medium- and large-scale instances of the problem, we first develop an exact algorithm that exploits the fact that real-life networks often have rather small diameters. Then we propose two conceptually different heuristic algorithms. Finally, we conduct computational experiments with real-world and synthetic network instances under various settings, which reveal interesting insights and demonstrate the advantages and limitations of the proposed models and algorithms.

Suggested Citation

  • Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2019. "Finding Critical Links for Closeness Centrality," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 367-389, April.
  • Handle: RePEc:inm:orijoc:v:31:y:2019:i:2:p:367-389
    DOI: 10.1287/ijoc.2018.0829
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    References listed on IDEAS

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    Cited by:

    1. Camur, Mustafa C. & Sharkey, Thomas C. & Vogiatzis, Chrysafis, 2023. "The stochastic pseudo-star degree centrality problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 525-539.
    2. Zhong, Haonan & Mahdavi Pajouh, Foad & A. Prokopyev, Oleg, 2023. "On designing networks resilient to clique blockers," European Journal of Operational Research, Elsevier, vol. 307(1), pages 20-32.
    3. Nasirian, Farzaneh & Mahdavi Pajouh, Foad & Balasundaram, Balabhaskar, 2020. "Detecting a most closeness-central clique in complex networks," European Journal of Operational Research, Elsevier, vol. 283(2), pages 461-475.
    4. Matsypura, Dmytro & Veremyev, Alexander & Pasiliao, Eduardo L. & Prokopyev, Oleg A., 2023. "Finding the most degree-central walks and paths in a graph: Exact and heuristic approaches," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1021-1036.
    5. Colin P. Gillen & Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "Fortification Against Cascade Propagation Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1481-1499, October.
    6. Ali Tosyali & Jeongsub Choi & Byunghoon Kim & Hoshin Lee & Myong K. Jeong, 2021. "A dynamic graph-based approach to ranking firms for identifying key players using inter-firm transactions," Annals of Operations Research, Springer, vol. 303(1), pages 5-27, August.

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