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In this paper we propose a social capital measure for individuals belonging to a social network. To do this, we use a game theoretical approach and so we suppose that these individuals are also involved in a cooperative TU-game modelling the economic or social interests that motivate their interactions. We propose as a measure of individual social capital the difference between the Myerson and the Shapley values of actors in the social network and explore the properties of such a measure. This definition is close to our previous measure of centrality (Gómez et al., 2003) and so in this paper we also study the relation between social capital and centrality, finding that this social capital measure can be considered as a vector magnitude with two additive components: centrality and positional externalities. Finally, several real political examples are used to show the agreement of our conclusions with the reality in these situations.

The article of record as published may be found at http://dx.doi.org/10.1007/s10479-007-0247-4 ; A family of cohesiveness measures, based on game theoretical concepts, is proposed for subgroups in social networks. Given a communication situation, consisting of a coalitional game and a graph, both defined on the same set of players-nodes, cohesiveness of a subset is defined as the proportion of their worth that the players in subset retain, when the originally deterministic (restricted) graph becomes a probabilistic one (in a specific manner). Conditions on the game are given to reach some desirable properties. ; "Plan Nacional de I+D+i" of the Spanish Government ; "Plan Nacional de I+D+i" of the Spanish Government project MTM2005-09184-C02-01