Centrality Measures in Networks
41 Pages Posted: 19 Mar 2016 Last revised: 12 Jun 2019
Date Written: June 1, 2019
We show that although the prominent centrality measures in network analysis make use of different information about nodes' positions, they all process that information in a very restrictive and identical way. They all spring from a common family that are characterized by the same axioms. In particular, they are all based on a additively separable and linear treatment of a statistic that captures a node's position in the network. Using such statistics on nodes' positions, we also characterize trees on which centrality measures all agree.
Keywords: Centrality, prestige, power, influence, networks, social networks, rankings, centrality measures
JEL Classification: D85, D13, L14, O12, Z13, C65
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