Borgatti, Stephen P. and Everett, Martin G.
(2006)
*A Graph-theoretic perspective on centrality.*
Social Networks, 28 (4).
pp. 466-484.
ISSN 0378-8733

## 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

Item Type: | Article |
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Subjects: | University of Westminster > Westminster Business School |

Depositing User: | Miss Nina Watts |

Date Deposited: | 18 Feb 2009 15:50 |

Last Modified: | 18 Feb 2009 15:50 |

URI: | http://westminsterresearch.wmin.ac.uk/id/eprint/6035 |

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