Local and consistent centrality measures in parameterized networks |
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| Affiliation: | 1. Université Clermont Auvergne, CNRS, CERDI, F-63000 Clermont-Ferrand, France;2. Department of Economics, Monash University, Australia;3. IFN, Sweden;1. Center for Economic Studies, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium;2. European center for advanced research in economics and statistics, Université Libre de Bruxelles, 42 Avenue Roosevelt, 1050 Brussel, Belgium;3. Departamento de Matemáticas, Facultade de Economía, Universidade de Vigo, Campus Lagaos-Marcosende, 36310 Vigo, Spain;1. Departamento de Teoría e Historia Económica, Universidad de Granada, Granada 18071, Spain;2. Departamento de Teoría e Historia Económica, Universidad de Málaga, 29071 Málaga, Spain;1. LAAS CNRS, France;2. IIT, Bombay, India;1. Public University of Navarre, Department of Economics, Campus Arrosadia, 31006 Pamplona, Spain;2. University of Vigo, Department of Statistics and Operations Research, Campus Lagoas-Marcosende, 36310 Vigo, Spain;3. University of Granada, Department of Economics, Campus la Cartuja, 18071 Granada, Spain |
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| 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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