Graph energy centrality: a new centrality measurement based on graph energy to analyse social networks

Abstract

Critical node identification, one of the key issues in social network analysis, is addressed in this article with the development of a new centrality metric termed graph energy centrality (GEC). The fundamental idea underlying this GEC measure is to give each vertex a centrality value based on the graph energy that results from vertex elimination. We show that the GEC of each vertex is asymptotically equal to two for cycle graphs and exactly equal to two for complete graphs. We further demonstrate that star graphs can be ranked using only two GEC values, whereas path graphs can be ranked using a maximum of ⌈n+1<inf>2</inf> ⌉ values. The proposed algorithm takes O(n3) time complexity to rank all vertices; hence an optimised algorithm is also being proposed considering only a few classes of graphs. The proposed algorithm ranks the nodes based on the collaborative measure of eigenvalues. © 2022 Inderscience Enterprises Ltd.. All rights reserved.