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arXiv · 1701.04790

A Graph Theoretic Analysis of Leverage Centrality

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

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Roger Vargas, Jr., Abigail Waldron, Anika Sharma, Rigoberto Flórez, Darren A. Narayan. 2017-01-17. A Graph Theoretic Analysis of Leverage Centrality. https://arxiv.org/abs/1701.04790

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