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Closeness centralization measure for two-mode data of prescribed sizes

Published online by Cambridge University Press:  22 July 2016

MATJAŽ KRNC ,
JEAN-SÉBASTIEN SERENI ,
RISTE ŠKREKOVSKI  and
ZELEALEM B. YILMA
MATJAŽ KRNC
Affiliation:
FAMNIT, University of Primorska, Koper, Slovenia (e-mail: matjaz.krnc@gmail.com)
JEAN-SÉBASTIEN SERENI
Affiliation:
CNRS (LORIA), Vandœuvre-lès-Nancy, France (e-mail: sereni@kam.mff.cuni.cz)
RISTE ŠKREKOVSKI
Affiliation:
Department of Mathematics, University of Ljubljana, and Faculty of information studies, Novo Mesto, and FAMNIT, University of Primorska, Koper, Slovenia (e-mail: skrekovski@gmail.com)
ZELEALEM B. YILMA
Affiliation:
Carnegie Mellon University Qatar, Doha, Qatar (e-mail: zyilma@qatar.cmu.edu)
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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.

Keywords

centralitycloseness centralitytwo-mode datanetworkgraphcomplex networkmeasure centralization
Type
Research Article
Information
Network Science , Volume 4 , Issue 4 , December 2016 , pp. 474 - 490
Copyright
Copyright © Cambridge University Press 2016 

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