Centrality Measures in Networks

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 networks on which centrality measures all agree. JEL Classification Codes: D85, D13, L14, O12, Z13, C65