Quasi-Laplacian centrality: A new vertex centrality measurement based on Quasi-Laplacian energy of networks

The measuring of vertex centrality, which determines the importance of vertices in a network, has been one of key issues in network analysis. Many classical methods have been already presented, such as degree, closeness, betweenness and PageRank centrality etc. In this paper, a new vertex centrality measurement called Quasi-Laplacian centrality is proposed. Our main idea is that the importance (centrality) of a vertex v is reflected by the variation of the Quasi-Laplacian energy responding to the deletion of the vertex v from the network. Furthermore, we prove that the Quasi-Laplacian energy of a network G is related not only to the number of edges in the original network G but also to the number of edges in its corresponding line graph L(G). Thus, the new presented Quasi-Laplacian centrality of a vertex v considers not only its position in the original graph G, but also its position in the line graph L(G). We further investigate the validness and robustness of this new centrality measure by applying this method to three classical social network data sets and 14 other data sets from various domains. And on all these networks, we obtain reliable and even better results by using the common-used Susceptible–Infected–Resistant (SIR) model, which provide the strong evidences of the new measure’s utility. Besides, this new Quasi-Laplacian centrality measurement has lower computing complexity than others except degree centrality, thus is expected to have promising applications to run on big data in the future.