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A centrality notion for graphs based on Tukey depth

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  • Cerdeira, J. Orestes
  • Silva, Pedro C.

Abstract

Centrality on graphs aims at ranking vertices in terms of their contribution to facilitate the communication flow in the network. Tukey depth is one of most widely used statistical measures to assess the centrality of a point within a cloud of points in the multidimensional space. In this paper we propose and discuss how to adapt Tukey depth to develop a novel centrality index for vertices of a graph. We present some properties of the indices on several classes of graphs, show that computing the indices is NP-hard, extend the indices to assess the centrality of group of vertices and give 0/1 linear formulations to calculate them.

Suggested Citation

  • Cerdeira, J. Orestes & Silva, Pedro C., 2021. "A centrality notion for graphs based on Tukey depth," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004987
    DOI: 10.1016/j.amc.2021.126409
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    References listed on IDEAS

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    1. Xiaohui Liu, 2017. "Fast implementation of the Tukey depth," Computational Statistics, Springer, vol. 32(4), pages 1395-1410, December.
    2. Wang, Juan & Li, Chao & Xia, Chengyi, 2018. "Improved centrality indicators to characterize the nodal spreading capability in complex networks," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 388-400.
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