Maintaining the duality of closeness and betweenness centrality
Maintaining the duality of closeness and betweenness centrality
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DOI：
10.1016/j.socnet.2015.08.003
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发表时间：
2016-01-01
期刊：
影响因子：
3.1
通讯作者：
Freeman, Linton C.
中科院分区：
文献类型：
--
作者：
Brandes, Ulrik;Borgatti, Stephen P.;Freeman, Linton C.
介数中心性通常被认为是其他节点对给定节点的依赖性的度量，因此也是潜在控制的度量。接近中心性通常被解释为对访问效率或对中介机构潜在控制的独立性的度量。介数和贴近度通常被认为是相关的原因有两个：第一，因为它们的概念上的二元性，相对于依赖性，第二，因为两者都是定义在最短路径，我们表明，这些想法的第一个-二元性-不仅是正确的，在一般的概念意义上，而且在精确的数学术语。当这两个索引以共享的二元依赖关系表示时，这一点变得显而易见。我们还表明，第二个想法-最短路径-是假的，因为它是不保存时，指数一般化使用的最短路径的标准定义值图。这揭示了封闭性作为独立性实际上不同于封闭性作为有效性，我们提出了一个不同的距离概念，它保持了封闭性作为独立性与中介性的二元性，也是在有价值的关系上。(C)2015 Elsevier B. V.版权所有。
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 closenessas-efficiency, and we propose a variant notion of distance that maintains the duality of closeness-as-independence with betweenness also on valued relations. (C) 2015 Elsevier B.V. All rights reserved.