Involve: A Journal of Mathematics

  • Involve
  • Volume 10, Number 4 (2017), 583-592.

Leverage centrality of knight's graphs and Cartesian products of regular graphs and path powers

Roger Vargas, Abigail Waldron, Anika Sharma, Rigoberto Flórez, and Darren A. Narayan

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In 2010, Joyce et al. defined the leverage centrality of a graph as a means to analyze connections within the brain. In this paper we investigate this property from a mathematical perspective and determine the leverage centrality for knight’s graphs, path powers, and Cartesian products.

Article information

Involve, Volume 10, Number 4 (2017), 583-592.

Received: 9 September 2015
Revised: 4 January 2016
Accepted: 25 March 2016
First available in Project Euclid: 12 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C07: Vertex degrees [See also 05E30]

leverage centrality knight's graphs


Vargas, Roger; Waldron, Abigail; Sharma, Anika; Flórez, Rigoberto; Narayan, Darren A. Leverage centrality of knight's graphs and Cartesian products of regular graphs and path powers. Involve 10 (2017), no. 4, 583--592. doi:10.2140/involve.2017.10.583.

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  • K. E. Joyce, P. J. Laurienti, J. H. Burdette, and S. Hayasaka, “A new measure of centrality for brain networks”, PLOS ONE 5:8 (2010), art. id. e12200.
  • C. Li, Q. Li, P. Van Mieghem, H. E. Stanley, and H. Wang, “Correlation between centrality metrics and their application to the opinion model”, Eur. Phys. J. B 88:3 (2015), art. id. 65.
  • A. Sharma, R. Vargas, A. Waldron, R. Florez, and D. A. Narayan, “Leverage centrality of graphs”, preprint, 2017.