Maintaining the duality of closeness and betweenness centrality

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Brandes_0-311031.pdf
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2016
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Borgatti, Stephen P.
Freeman, Linton C.
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Social Networks. 2016, 44, pp. 153-159. ISSN 0378-8733. eISSN 1879-2111. Available under: doi: 10.1016/j.socnet.2015.08.003
Zusammenfassung

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.

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004 Informatik
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Betweenness centrality, Closeness centrality, Duality, Dependency, Derived relations
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ISO 690BRANDES, Ulrik, Stephen P. BORGATTI, Linton C. FREEMAN, 2016. Maintaining the duality of closeness and betweenness centrality. In: Social Networks. 2016, 44, pp. 153-159. ISSN 0378-8733. eISSN 1879-2111. Available under: doi: 10.1016/j.socnet.2015.08.003
BibTex
@article{Brandes2016Maint-32317,
  year={2016},
  doi={10.1016/j.socnet.2015.08.003},
  title={Maintaining the duality of closeness and betweenness centrality},
  volume={44},
  issn={0378-8733},
  journal={Social Networks},
  pages={153--159},
  author={Brandes, Ulrik and Borgatti, Stephen P. and Freeman, Linton C.}
}
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