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 an identical way. They are all based on a additively separable and linear treatment of a statistic that captures a node's position in the network. We then add axioms that tie down the nodal statistics that are used to characterize two types of centrality measures: degree centrality and weighted measures that depend only upon the number of nodes at various distances from a given node (neighborhood statistics). Using such statistics on nodes' positions, we also characterize trees on which centrality measures all agree.

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