Centrality Measures in Networks

36 Pages Posted: 19 Mar 2016 Last revised: 18 Jun 2017

See all articles by Francis Bloch

Francis Bloch

French National Center for Scientific Research (CNRS) - Research Group in Quantitative Saving (GREQAM); National Center for Scientific Research (CNRS)

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)

Pietro Tebaldi

University of Chicago - Department of Economics

Date Written: June 1, 2017

Abstract

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.

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

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

Suggested Citation

Bloch, Francis and Jackson, Matthew O. and Tebaldi, Pietro, Centrality Measures in Networks (June 1, 2017). Available at SSRN: https://ssrn.com/abstract=2749124 or http://dx.doi.org/10.2139/ssrn.2749124

Francis Bloch

French National Center for Scientific Research (CNRS) - 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

Canadian Institute for Advanced Research (CIFAR) ( email )

180 Dundas Street West, Suite 1400
Toronto, Ontario
Canada

Pietro Tebaldi

University of Chicago - Department of Economics ( email )

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

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