The normalized incidence energy of a graph

The energy of a graph G is the sum of the singular values of its adjacency matrix. It is a graph invariant used in mathematical chemistry. The normalized incidence energy of the graph G, denoted by NIE(G), is defined as the sum of the singular values of its normalized incidence matrix. We find some upper and lower bounds and determine the Coulson integral formula for NIE(G). Based on the integral formula, we give a way to compare the normalized incidence energies. Moreover we show a relation between normalized incidence energy and Randić energy.