A Graph Theoretic Analysis of Leverage Eccentricity Centrality

Abstract

In complex networks, the identification of key regions is determined through centrality measures. There are various centrality measures in which leverage centrality is specially designed for neural network. The concept of leverage centrality is the relationship between degree of a vertex relative to its neighbours and it operates under the principle that a vertex in a network is central if its immediate neighbours rely on it for information. In this paper, we built upon leverage centrality and introduce leverage eccentricity centrality, which is a measure of how eccentricity of a vertex rely on the eccentricity of all its neighbours. We investigate this property from a mathematical perspective. We first outline some of the basic properties and then compute leverage eccentricity centrality of vertices in different families of graphs, line graph of some special graphs, Mycielskian of some standard graphs, and molecular graph of cyclo-hydrocarbons.