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A Modified Myerson Value for Determining the Centrality of Graph Vertices

  • MATHEMATICAL GAME THEORY AND APPLICATIONS
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Abstract

To analyze the structure of social networks, the methods of cooperative game theory can be adopted. One of such methods is based on the calculation of the Myerson values as a centrality measure of the vertices in a graph. In this case, the number of paths of a certain length in the subgraphs corresponding to the coalitions is used as the characteristic function. This paper proposes a modification of the Myerson value for the case where the paths in a graph containing cycles are included in consideration. The effectiveness of this approach is illustrated by several examples.

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Funding

This work was partially supported by the “Double Hundred Talent Plan” of Shandong Province, project no. WST2017009.

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Authors and Affiliations

  1. Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, Petrozavodsk, 185910, Russia

    V. V. Mazalov

  2. School of Mathematics and Statistics, Qingdao University, Qingdao, China

    V. V. Mazalov

  3. Institute of Applied Mathematics of Shandong, Qingdao, China

    V. V. Mazalov

  4. Institute of Mathematics and Information Technology, Petrozavodsk State University, Petrozavodsk, 185910, Russia

    V. A. Khitraya

Authors
  1. V. V. Mazalov
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  2. V. A. Khitraya
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Correspondence to V. V. Mazalov or V. A. Khitraya.

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Mazalov, V.V., Khitraya, V.A. A Modified Myerson Value for Determining the Centrality of Graph Vertices. Autom Remote Control 82, 145–159 (2021). https://doi.org/10.1134/S0005117921010100

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  • DOI: https://doi.org/10.1134/S0005117921010100

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