Centrality and power in social networks: a game theoretic approach

Abstract

A new family of centrality measures, based on game theoretical concepts, is proposed for social networks. To reflect the interests that motivate the interactions among individuals in a network, a cooperative game in characteristic function form is considered. From the graph and the game, the graph-restricted game is obtained. Shapley value in a game is considered as actor's power. The difference between actor's power in the new game and his/her power in the original one is proposed as a centrality measure. Conditions are given to reach some desirable properties. Finally, a decomposition is proposed.