A graph theoretic analysis of leverage centrality. Issue 3 (1st December 2017)

• Record Type: Journal Article
• Authors: Vargas, Roger; Waldron, Abigail; Sharma, Anika; Flórez, Rigoberto; Narayan, Darren A.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 14:Issue 3(2017)
• Page Start: 295
• Page End: 306
• Publication Date: 2017-12-01
• Subjects: Centrality -- Degrees -- Triangle numbers
• DOI: 10.1016/j.akcej.2017.05.001
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: In 2010, Joyce et al. defined the leverage centrality of vertices in a graph as a means to analyze functional connections within the human brain. In this metric a degree of a vertex is compared to the degrees of all it neighbors. We investigate this property from a mathematical perspective. We first outline some of the basic properties and then compute leverage centralities of vertices in different families of graphs. In particular, we show there is a surprising connection between the number of distinct leverage centralities in the Cartesian product of paths and the triangle numbers.