Closeness centralization measure for two-mode data of prescribed sizes

Matjaž Krnc, Jean-Sébastien Sereni, Riste Škrekovski and Zelealem B. Yilma

Network Science, 2016, vol. 4, issue 4, 474-490

Abstract: We confirm a conjecture by Everett et al. (2004) regarding the problem of maximizing closeness centralization in two-mode data, where the number of data of each type is fixed. Intuitively, our result states that among all networks obtainable via two-mode data, the largest closeness is achieved by simply locally maximizing the closeness of a node. Mathematically, our study concerns bipartite graphs with fixed size bipartitions, and we show that the extremal configuration is a rooted tree of depth 2, where neighbors of the root have an equal or almost equal number of children.

Date: 2016
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