Centrality Measures in Networks

TL;DR

This paper provides a taxonomy of network centrality measures based on their use of node position information, revealing how different measures relate and under what conditions they agree.

Contribution

It introduces a unifying framework for centrality measures by classifying them along two key dimensions related to node position information and its weighting.

Findings

Centrality measures are based on additive, linear treatments of node position statistics.

A taxonomy categorizes measures by information use and weighting functions.

Conditions under which different centrality measures agree are characterized.

Abstract

We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality measures that distills them to varying on two dimensions: (i) which information they make use of about nodes' positions, and (ii) how that information is weighted as a function of distance from the node in question. The three sorts of information about nodes' positions that are usually used -- which we refer to as "nodal statistics" -- are the paths from a given node to other nodes, the walks from a given node to other nodes, and the geodesics between other nodes that include a given node. Using such statistics on nodes' positions, we also characterize the types of trees such that centrality measures all agree, and we also discuss the properties that identify some path-based centrality measures.