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Mathematical properties of Q-measures

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  • Rousseau, Ronald
  • Liu, Yuxian
  • Guns, Raf

Abstract

Q-measures are network indicators that gauge a node's brokerage role between different groups in the network. Previous studies have focused on their definition for different network types and their practical application. Little attention has, however, been paid to their theoretical and mathematical characterization. In this article we contribute to a better understanding of Q-measures by studying some of their mathematical properties in the context of unweighted, undirected networks. An external Q-measure complementing the previously defined local and global Q-measure is introduced. We prove a number of relations between the values of the global, the local and the external Q-measure and betweenness centrality, and show how the global Q-measure can be rewritten as a convex decomposition of the local and external Q-measures. Furthermore, we formally characterize when Q-measures obtain their maximal value. It turns out that this is only possible in a limited number of very specific circumstances.

Suggested Citation

  • Rousseau, Ronald & Liu, Yuxian & Guns, Raf, 2013. "Mathematical properties of Q-measures," Journal of Informetrics, Elsevier, vol. 7(3), pages 737-745.
    • Handle: RePEc:eee:infome:v:7:y:2013:i:3:p:737-745
    DOI: 10.1016/j.joi.2013.06.002
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    References listed on IDEAS

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    1. Risse, Thomas, 2000. "“Let's Argue!”: Communicative Action in World Politics," International Organization, Cambridge University Press, vol. 54(1), pages 1-39, January.
    2. Erjia Yan & Ying Ding, 2009. "Applying centrality measures to impact analysis: A coauthorship network analysis," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 60(10), pages 2107-2118, October.
    3. Raf Guns & Yu Xian Liu & Dilruba Mahbuba, 2011. "Q-measures and betweenness centrality in a collaboration network: a case study of the field of informetrics," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(1), pages 133-147, April.
    4. Rousseau, Ronald & Liu, Yuxian & Ye, Fred Y., 2012. "A preliminary investigation on diffusion through a layered system," Journal of Informetrics, Elsevier, vol. 6(2), pages 177-191.
    5. Liu, Yuxian & Rousseau, Ronald & Guns, Raf, 2013. "A layered framework to study collaboration as a form of knowledge sharing and diffusion," Journal of Informetrics, Elsevier, vol. 7(3), pages 651-664.
    6. Lixin Chen & Ronald Rousseau, 2008. "Q-measures for binary divided networks: Bridges between German and English institutes in publications of the Journal of Fluid Mechanics," Scientometrics, Springer;Akadémiai Kiadó, vol. 74(1), pages 57-69, January.
    7. Ronald Rousseau & Lin Zhang, 2008. "Betweenness centrality and Q-measures in directed valued networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 75(3), pages 575-590, June.
    8. Loet Leydesdorff, 2007. "Betweenness centrality as an indicator of the interdisciplinarity of scientific journals," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(9), pages 1303-1319, July.
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    Cited by:

    1. Xian Li & Dangzhi Zhao & Xiaojun Hu, 2020. "Gatekeepers in knowledge transfer between science and technology: an exploratory study in the area of gene editing," Scientometrics, Springer;Akadémiai Kiadó, vol. 124(2), pages 1261-1277, August.
    2. Rousseau, Ronald & Liu, Yuxian & Guns, Raf, 2014. "An addendum and correction to “Mathematical properties of Q-measures” (vol. 7, issue 3, pp. 737–745)," Journal of Informetrics, Elsevier, vol. 8(3), pages 486-490.

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