Phased graphs and graph energies - Klein, Douglas J.; Rosenfeld, Vladimir R. (Journal of mathematical chemistry, 2011)
We define a phased graph G to yield an adjacency matrix A ( G ) having general magnitude-1 values in the same locations as the usual unphased case, but subject to the restriction that A be Hermitian. Some characteristics of such phased graphs and their eigenspectra are contemplated and to some extent described. Different graph energies are defined as suitable sums over adjacency-matrix eigenvalues, with “occupation-number” coefficients .