  In non-Hermitian coulped-resonator networks, the eigenvectors of degenerate
eigenmodes may become parallel due to the singularity at so-called Exceptional
Points (EP). To exploit the parametric sensitivity at EPs, an important problem
is, given an arbitrary set of coupled resonators, how to generate a desired EP
by properly coupling them together. This paper provides the solution for the
case of three resonators. We show that all physically admissible EPs can be
realized with either weakly coupled linear networks or strongly coupled
circular networks, and the latter type of EPs has not been reported in the
literature. Each admissible EP eigenvalue can be realized by two and only two
resonator networks, and the formulas for calculating the required coupling
constants are provided. The characteristics of these EPs are illustrated by the
change of transmission spectra near them, which verify the enhanced sensitivity
induced by the singularity of EPs.
