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Game-Theoretic Centrality of Directed Graph Vertices

  • MATHEMATICAL GAME THEORY AND APPLICATIONS
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Abstract

The paper considers a game theory approach to calculating the centrality value of the vertices in a directed graph, based on the number of vertex occurrences in fixed length paths. It is proposed to define vertex centrality as a solution of a cooperative game, where the characteristic function is given as the number of simple paths of fixed length in subgraphs corresponding to coalitions. The concept of integral centrality is introduced as the value of a definite integral of the payoff function. It is shown that this centrality measure satisfies the Boldi–Vigna axioms.

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Funding

This work was supported by the Russian Science Foundation, project no. 22-11-20015 implemented in collaboration with Republic of Karelia authorities with funding from the Republic of Karelia Venture Capital Fund.

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Authors and Affiliations

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

    V. A. Khitraya & V. V. Mazalov

  2. Institute of Mathematics and Information Technologies, Petrozavodsk State University, Petrozavodsk, Russia

    V. A. Khitraya

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

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Khitraya, V.A., Mazalov, V.V. Game-Theoretic Centrality of Directed Graph Vertices. Autom Remote Control 85, 225–237 (2024). https://doi.org/10.1134/S0005117924020061

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