Aleskerov proposes new centrality indices based on power indices, which take into account preferences of agents for coalition formation proposed for an analysis of power distribution in elected bodies. These indices reveal most influential (central) nodes in networks and take into account the parameters of the nodes in networks, a possibility of group influence from the subset of nodes to single nodes, and intensity of short and long interactions among the nodes. Several applications are studied - networks of conflicts, migration, financial networks, citation networks, etc.