A model of influence in a social network.

In the paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the Hoede-Bakker index - the notion which computes the overall decisional "power" of a player in a social network. The main drawback of the Hoede-Bakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we separate the influence part from the group decision part, and focus on the description and analysis of the influence part. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations. Finally, we propose a suitable definition of a modified decisional power.