Maintaining the duality of closeness and betweenness centrality

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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.} }

2016 Maintaining the duality of closeness and betweenness centrality Freeman, Linton C. 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.<br /><br />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. Borgatti, Stephen P. Brandes, Ulrik terms-of-use Freeman, Linton C. 2015-12-03T10:05:29Z Brandes, Ulrik eng Borgatti, Stephen P. 2015-12-03T10:05:29Z

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