Centrality Measures in Networks

44 Pages Posted: 19 Mar 2016 Last revised: 10 Aug 2021

See all articles by Francis Bloch

Francis Bloch

University of Angers - Research Group in Quantitative Saving (GREQAM); National Center for Scientific Research (CNRS)

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute

Pietro Tebaldi

University of Chicago - Department of Economics

Date Written: June 1, 2019

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.

Keywords: Centrality, prestige, power, influence, networks, social networks, rankings, centrality measures

JEL Classification: D85, D13, L14, O12, Z13, C65

Suggested Citation

Bloch, Francis and Bloch, Francis and Jackson, Matthew O. and Tebaldi, Pietro, Centrality Measures in Networks (June 1, 2019). Available at SSRN: https://ssrn.com/abstract=2749124 or http://dx.doi.org/10.2139/ssrn.2749124

Francis Bloch

University of Angers - Research Group in Quantitative Saving (GREQAM) ( email )

Centre de la Vieille Charité
2, rue de la Charité
Marseille, 13002
France

National Center for Scientific Research (CNRS) ( email )

54, boulevard Raspail
Paris, 75006
France

Matthew O. Jackson (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
1-650-723-3544 (Phone)

HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Pietro Tebaldi

University of Chicago - Department of Economics ( email )

1126 E. 59th St
Chicago, IL 60637
United States

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