A Graph Theoretic Analysis of Leverage Centrality
Combinatorics
2017-01-18 v1
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.
Cite
@article{arxiv.1701.04790,
title = {A Graph Theoretic Analysis of Leverage Centrality},
author = {Roger Vargas, and Abigail Waldron and Anika Sharma and Rigoberto Flórez and Darren A. Narayan},
journal= {arXiv preprint arXiv:1701.04790},
year = {2017}
}
Comments
13 pages