A Graph-theoretic perspective on centrality

Stephen P. Borgatti, Martin G. Everett

Research output: Contribution to journalArticlepeer-review

1099 Scopus citations

Abstract

The concept of centrality is often invoked in social network analysis, and diverse indices have been proposed to measure it. This paper develops a unified framework for the measurement of centrality. All measures of centrality assess a node's involvement in the walk structure of a network. Measures vary along four key dimensions: type of nodal involvement assessed, type of walk considered, property of walk assessed, and choice of summary measure. If we cross-classify measures by type of nodal involvement (radial versus medial) and property of walk assessed (volume versus length), we obtain a four-fold polychotomization with one cell empty which mirrors Freeman's 1979 categorization. At a more substantive level, measures of centrality summarize a node's involvement in or contribution to the cohesiveness of the network. Radial measures in particular are reductions of pair-wise proximities/cohesion to attributes of nodes or actors. The usefulness and interpretability of radial measures depend on the fit of the cohesion matrix to the one-dimensional model. In network terms, a network that is fit by a one-dimensional model has a core-periphery structure in which all nodes revolve more or less closely around a single core. This in turn implies that the network does not contain distinct cohesive subgroups. Thus, centrality is shown to be intimately connected with the cohesive subgroup structure of a network.

Original languageEnglish
Pages (from-to)466-484
Number of pages19
JournalSocial Networks
Volume28
Issue number4
DOIs
StatePublished - Oct 2006

ASJC Scopus subject areas

  • Anthropology
  • Sociology and Political Science
  • General Social Sciences
  • General Psychology

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