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The Key Class in Networks

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  • Nizar Allouch
  • Jayeeta Bhattacharya

Abstract

This paper proposes new centrality measures to characterise the `key class', when agents in a network are sorted into role-equivalent classes, such that its removal results in an optimal change in the network activity. The notion of role-equivalence is defined through the graph-theoretical concept of equitable partition of networks, which finds wide empirical and theoretical applicability. Players in the network engage in a non-cooperative game with local payoff complementarities. We establish a link between the generic network and its partitioned or quotient graph, and use it to relate the Nash equilibrium activity of classes with their position within the partitioned network. The result informs two class-based centrality measures that geometrically characterise the key class for an optimal reduction (or increase) in the aggregate and the per-capita network activity, respectively.

Suggested Citation

  • Nizar Allouch & Jayeeta Bhattacharya, 2021. "The Key Class in Networks," Studies in Economics 2110, School of Economics, University of Kent.
    • Handle: RePEc:ukc:ukcedp:2110
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    File URL: https://www.kent.ac.uk/economics/repec/2110.pdf
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    References listed on IDEAS

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    7. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves & Lee, Lung-Fei, 2011. "Criminal Networks: Who is the Key Player?," Research Papers in Economics 2011:7, Stockholm University, Department of Economics.
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    More about this item

    Keywords

    Social and economic networks; network games; equitable partition; centrality measures;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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