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The Key Class in Networks

Nizar Allouch and Jayeeta Bhattacharya

Studies in Economics from School of Economics, University of Kent

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.

Keywords: Social and economic networks; network games; equitable partition; centrality measures (search for similar items in EconPapers)
JEL-codes: C72 D85 (search for similar items in EconPapers)
Date: 2021-08
New Economics Papers: this item is included in nep-gth, nep-soc and nep-ure
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