Correlations Between Network Vulnerability and Laplacian Energies

Abstract

In the network analysis, vulnerability plays key role. Similarly, Laplacian matrices are also effective tools in network analysis. In this study, we examine correlations between those two concepts. We first calculate the well-known vulnerability measures called edge connectivity, vertex connectivity, and solitude number. Then, we find correlation between vulnerability measures and energies of Laplacian matrices. As a result, we find strong correlations between Laplacian energies and vertex connectivity of a network.