A Graph-theoretic perspective on centrality

Borgatti, S.P. and Everett, M.G. 2006. A Graph-theoretic perspective on centrality. Social Networks. 28 (4), pp. 466-484.

TitleA Graph-theoretic perspective on centrality
AuthorsBorgatti, S.P. and Everett, M.G.
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

JournalSocial Networks
Journal citation28 (4), pp. 466-484
ISSN0378-8733
YearOct 2006
PublisherElsevier
Digital Object Identifier (DOI)doi:10.1016/j.socnet.2005.11.005
Publication dates
PublishedOct 2006

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