The Key Class in Networks

This paper proposes new centrality measures to characterise the ‘key class’, whose removal results in maximal reduction in the network activity, when agents in a network are sorted into role-equivalent classes. 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 noncooperative 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 inducing an optimal change in the aggregate and the per-capita network activity, respectively