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Closeness Centralization Measure for Two-mode Data of Prescribed Sizes

Abstract : We confirm a conjecture by Everett, Sinclair, and Dankelmann [Some Centrality results new and old, J. Math. Sociology 28 (2004), 215–227] 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.
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https://hal.inria.fr/hal-01289470
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Submitted on : Wednesday, March 16, 2016 - 5:17:04 PM
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Matjaž Krnc, Jean-Sébastien Sereni, Ristě Skrekovski, Zelealem Yilma. Closeness Centralization Measure for Two-mode Data of Prescribed Sizes. Network Science, Cambridge University Press, 2016, 4 (4), pp.474 - 490. ⟨10.1017/nws.2016.14⟩. ⟨hal-01289470⟩

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