Energy of weighted digraphs

In this paper, we study the spectra of weighted digraphs, where weights are taken from the set of non zero real numbers. We obtain formulae for the characteristic polynomial of two families of weighted bipartite digraphs. We study the sign alternating property of coefficients of characteristic polynomial in some classes of weighted digraphs. We extend the concept of energy to weighted digraphs and obtain Coulson's integral formula. As a consequence of these results, we study energy comparison property by means of a quasi-order relation. Unicyclic weighted digraphs with cycle-weight r∈[−1,1]∖{0} having minimum and maximum energy are characterized. Finally, we obtain well known McClelland upper bound for the energy of weighted digraphs and also an upper bound for the energy of a weighted digraph in terms of number of arcs and their weights.