Lower bounds for the Estrada index using mixing time and Laplacian spectrum

Abstract

The logarithm of the Estrada index has been recently proposed as a spectral measure to characterize the robustness of complex networks. We derive novel analytic lower bounds for the logarithm of the Estrada index based on the Laplacian spectrum and the mixing times of random walks on the network. The main techniques employed are some inequalities, such as the thermodynamic inequality in statistical mechanics, a trace inequality of von Neumann, and a refined harmonic-arithmetic mean inequality.