Estrada index of general weighted graphs

Abstract

Let G be a general weighted graph (with possible self-loops) on n vertices and λ1,λ2,.... ,λn be its eigenvalues. The Estrada index of G is a graph invariant defined as EE=∑i=1neλi. We present a generic expression for EE based on weights of short closed walks in G. We establish lower and upper bounds for EEin terms of low-order spectral moments involving the weights of closed walks. A concrete example of calculation is provided. © 2012 Australian Mathematical Publishing Association Inc.