Local and consistent centrality measures in parameterized networks

Wepropose an axiomatic approach to characterize centrality measures for which the centrality of an agentis recursively related to the centralities of the agents she is connected to. This includes the Katz–Bonacichand the eigenvector centrality. The core of our argument hinges on the power of the consistency axiom,which relates the properties of the measure for a given network to its properties for a reduced problem.In our case, the reduced problem only keeps track of local and parsimonious information. Our axiomaticcharacterization highlights the conceptual similarities among those measures