Maintaining the duality of closeness and betweenness centrality

Brandes, Ulrik; Borgatti, Stephen P.; Freeman, Linton C.

Maintaining the duality of closeness and betweenness centrality

Dateien

Brandes_0-311031.pdfGröße: 457.2 KBDownloads: 2971

Datum

2016

Autor:innen

Brandes, Ulrik

Borgatti, Stephen P.

Freeman, Linton C.

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

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.

Fachgebiet (DDC)

004 Informatik

Schlagwörter

Betweenness centrality, Closeness centrality, Duality, Dependency, Derived relations

Zitieren

ISO 690

BRANDES, 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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