Local and Consistent Centrality Measures in Networks

The centrality of an agent in a network has been shown to be crucial in explaining different behaviors and outcomes. In this paper, we propose an axiomatic approach to characterize a class of centrality measures for which the centrality of an agent is recursively related to the centralities of the agents she is connected to. This includes the Katz-Bonacich and 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. This is possible because all the centralities study here are local in the sense that the centrality measure of an agent only depends on her set of neighbors and their centralities. Our axiomatic characterization highlights the conceptual similarities among this class of measures.