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Partial orders for zero-sum arrays with applications to network theory

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  • Liu, Yuxian
  • Rousseau, Ronald
  • Egghe, Leo

Abstract

In this contribution we study partial orders in the set of zero-sum arrays. Concretely, these partial orders relate to local and global hierarchy and dominance theories. The exact relation between hierarchy and dominance curves is explained. Based on this investigation we design a new approach for measuring dominance or stated otherwise, power structures, in networks. A new type of Lorenz curve to measure dominance or power is proposed, and used to illustrate intrinsic characteristics of networks. The new curves, referred to as D-curves are partly concave and partly convex. As such they do not satisfy Dalton’s transfer principle. Most importantly, this article introduces a framework to compare different power structures as a whole.

Suggested Citation

  • Liu, Yuxian & Rousseau, Ronald & Egghe, Leo, 2017. "Partial orders for zero-sum arrays with applications to network theory," Journal of Informetrics, Elsevier, vol. 11(1), pages 257-274.
    • Handle: RePEc:eee:infome:v:11:y:2017:i:1:p:257-274
    DOI: 10.1016/j.joi.2016.11.006
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    References listed on IDEAS

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