Generalization of certain centrality measures for social networks analysis

No doubt, the majority of people have personal accounts on several social networks, which allow them to exchange information with their family and friends and to follow their interests.  A social network can be defined by a set of social entities and the relationships that these social entities have with each other directly, or indirectly through the length of the links between them.  For a better understanding the interest of the social communication between people, which is the main key for the process of social network analysis, we will use indicators that are supposed to determine the notion of importance in a network by identifying the most significant entities, called Centrality measures.  The idea of this paper is to generalize these measures and rewrite them in a new way in order to analyze the importance of social networks through the number of their levels.