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

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Official URL: http://dx.doi.org/10.1016/j.socnet.2005.11.005

## 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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Research Community: | University of Westminster > Westminster Business School |

ID Code: | 6035 |

Deposited On: | 18 Feb 2009 15:50 |

Last Modified: | 18 Feb 2009 15:50 |

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