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# Maintaining the duality of closeness and betweenness centrality

Type of Publication: | Journal article |

Publication status: | Published |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-311031 |

Author: | Brandes, Ulrik; Borgatti, Stephen P.; Freeman, Linton C. |

Year of publication: | 2016 |

Published in: | Social Networks ; 44 (2016). - pp. 153-159. - ISSN 0378-8733. - eISSN 1879-2111 |

DOI (citable link): | https://dx.doi.org/10.1016/j.socnet.2015.08.003 |

Summary: |
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. |

Subject (DDC): | 004 Computer Science |

Keywords: | Betweenness centrality, Closeness centrality, Duality, Dependency, Derived relations |

Link to License: | Terms of use |

Bibliography of Konstanz: | Yes |

Checksum:
MD5:bd9d7437a7c8ced9b9c2746643886dc3

BRANDES, Ulrik, Stephen P. BORGATTI, Linton C. FREEMAN, 2016. Maintaining the duality of closeness and betweenness centrality. In: Social Networks. 44, pp. 153-159. ISSN 0378-8733. eISSN 1879-2111. Available under: doi: 10.1016/j.socnet.2015.08.003

@article{Brandes2016Maint-32317, title={Maintaining the duality of closeness and betweenness centrality}, year={2016}, doi={10.1016/j.socnet.2015.08.003}, volume={44}, issn={0378-8733}, journal={Social Networks}, pages={153--159}, author={Brandes, Ulrik and Borgatti, Stephen P. and Freeman, Linton C.} }

Brandes_0-311031.pdf | 172 |