Graph theory approach to exceptional points in wave scattering

In this paper, we use graph theory to solve wave scattering problems in the discrete dipole approximation. As a key result of this work, in the presence of active scatterers, we show how one can find arbitrary large–order zero eigenvalue exceptional points (EPs) in parameter space by solving a set of non–linear equations. We interpret these equations in a graph theory picture as vanishing sums of scattering events. We also show how the total field of the system responds to parameter perturbations at the EP. Finally, we investigate the sensitivity of the power output to imaginary perturbation in the design frequency. This perturbation can be employed to trade sensitivity for a different dissipation balance of the system.

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