Local and consistent centrality measures in parameterized networks
Abstract
We propose an axiomatic approach to characterize 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. Our axiomatic
characterization highlights the conceptual similarities among those measures.
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