Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T08:45:29.997Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bavelas, A. (1950). Communication patterns in task-oriented groups. The Journal of the Acoustical Society of America, 22 (6), 725–730.Google Scholar
Beauchamp, M. (1965). An improved index of centrality. Behavioral Science, 10 (2), 161–163.Google Scholar
Bell, J. R. (2014). Subgroup centrality measures. Network Science, 2 (02), 277–297.Google Scholar
Botafogo, R. A., Rivlin, E., & Shneiderman, B. (1992). Structural analysis of hypertexts: Identifying hierarchies and useful metrics. Acm Transactions on Information Systems, 10 (2), 142–180.CrossRefGoogle Scholar
Brandes, U., & Erlebach, T. (2005). Network analysis: Methodological foundations, Vol. 3418. Berlin Heidelberg: Springer Science & Business Media.Google Scholar
Davis, A., Gardner, B. B., & Gardner, M. R. (1969). Deep south. University of Chicago Press.Google Scholar
Everett, M. G., Sinclair, P., & Dankelmann, P. (2004). Some centrality results new and old. The Journal of Mathematical Sociology, 28 (4), 215–227.CrossRefGoogle Scholar
Freeman, L. C. (1979). Centrality in social networks conceptual clarification. Social Networks, 1 (3), 215–239.Google Scholar
Koschützki, D., Lehmann, K. A., Peeters, L., Richter, S., Tenfelde-Podehl, D., & Zlotowski, O. (2005). Centrality indices. Network analysis (pp. 16–61). Berlin Heidelberg: Springer.Google Scholar
Krnc, M., Sereni, J.-S., Škrekovski, R., & Yilma, Z. B. (2015). Eccentricity of networks with structural constraints. Submitted for publication.Google Scholar
Moxley, R. L., & Moxley, N. F. (1974). Determining point-centrality in uncontrived social networks. Sociometry, 37 (1), 122–130.Google Scholar
Newman, M. E. J., & Park, J. (2003). Why social networks are different from other types of networks. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 68 (3), 036122.Google Scholar
Nieminen, U. J. (1973). On the centrality in a directed graph. Social Science Research, 2 (4), 371–378.CrossRefGoogle Scholar
Sabidussi, G. (1966). The centrality index of a graph. Psychometrika, 31 (4), 581–603.Google Scholar
Sinclair, P. (2004). Betweenness centralization for bipartite graphs. The Journal of Mathematical Sociology, 29 (1), 25–31.Google Scholar
Valente, T. W., & Foreman, R. K. (1998). Integration and radiality: Measuring the extent of an individual's connectedness and reachability in a network. Social Networks, 20 (1), 89–105.CrossRefGoogle Scholar