Mathematical Perspectives of Leverage Centrality: A Review

Objectives: 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 networks. In this article, we review all the recent research works on leverage centrality, focusing mainly on its mathematical perspective. Further, our present research work and the future scope of leverage centrality are given. Methods: For this systematic review, we referred all the relevant articles in this area from 2019 to till present. Findings: Leverage centrality analysis of some infrastructure networks and group leverage centrality are recently investigated. At the application level, leverage centrality has been used in the analysis of functional magnetic resonance imaging (fMRI) data, and real-world networks including airline connections, electrical power grids, co-authorship collaborations, molecular interaction networks, and sparse complex networks. Novelty: Brain networks have demonstrated hierarchical structure and may be decomposed into modules or neighborhoods of nodes that perform similar processes. A novel centrality metric called leverage centrality proposed by Joyce et al. may be of particular use in such hierarchical networks as an aid in identifying hubs, nodes that are important to maintaining local topological structure. Keywords: Centrality Measure, Neural Network, Fmri, Hubs, Group Leverage Centrality