Eigenvalues of the normalized complex Laplacian for finite electrical networks [report]

Anna Muranova, Robert Schippa
The spectrum of the normalized complex Laplacian for electrical networks is analyzed. We show that eigenvalues lie in a larger region compared to the case of the real Laplacian. We show the existence of eigenvalues with negative real part and absolute value greater than $2$. An estimate from below for the first non-vanishing eigenvalue in modulus is provided. We supplement the estimates with examples, showing sharpness.
doi:10.5445/ir/1000130241 fatcat:jaihf3tasjh7rcmed7dnr4im5y