Maintaining the duality of closeness and betweenness centrality

Ulrik Brandes, Stephen P. Borgatti, Linton C. Freeman

Research output: Contribution to journalArticlepeer-review

160 Scopus citations

Abstract

Betweenness centrality is generally regarded as a measure of others' dependence on a given node, and therefore as a measure of potential control. Closeness centrality is usually interpreted either as a measure of access efficiency or of independence from potential control by intermediaries. Betweenness and closeness are commonly assumed to be related for two reasons: first, because of their conceptual duality with respect to dependency, and second, because both are defined in terms of shortest paths. We show that the first of these ideas - the duality - is not only true in a general conceptual sense but also in precise mathematical terms. This becomes apparent when the two indices are expressed in terms of a shared dyadic dependency relation. We also show that the second idea - the shortest paths - is false because it is not preserved when the indices are generalized using the standard definition of shortest paths in valued graphs. This unveils that closeness-as-independence is in fact different from closeness-as-efficiency, and we propose a variant notion of distance that maintains the duality of closeness-as-independence with betweenness also on valued relations.

Original languageEnglish
Pages (from-to)153-159
Number of pages7
JournalSocial Networks
Volume44
DOIs
StatePublished - Jan 1 2016

Bibliographical note

Funding Information:
This research was partially supported by Deutsche Forschungsgemeinschaft (DFG) under grant Br 2158/6-1 .

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

  • Betweenness centrality
  • Closeness centrality
  • Dependency
  • Derived relations
  • Duality

ASJC Scopus subject areas

  • Anthropology
  • Sociology and Political Science
  • Social Sciences (all)
  • Psychology (all)

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