On Laplacian centrality of a graph: An exposition - Inguillo, Margaret C. (Animo Repository, 2023)
A graph is viewed as a combinatorial representation of existing relations among objects where we call the objects vertices and the relations edges. The importance of a vertex in a graph or vertex centrality can be measured according to the number of neighbours of a vertex (degree), how close one vertex is to the other (closeness), the frequency of a certain vertex being passed by other vertices (betweenness), or how one vertex has influenced by the vertex’s connections (eigenvector). In 2012, Qi et. al. proposed a new centrality measurement known as the Laplacian centrality, which measures the centrality based on how the vertex has affected the whole network or graph after its deletion. In this paper, we give an exposition focusing on the proposed measurement that will benefit future researchers by the provision of additional details on the established results of the said new centrality measure. The main results of Qi et. al. are illustrated using sample social networks found on a network repository. Using Python, we compute the Laplacian energy and Laplacian centrality in our sample social networks.