This paper deals with explicit analytical dependencies between all coefficients of the closed-loop characteristic polynomial and all entries of the output feedback matrix. First, a special kind of non-linear relation that occurs is explained. Next, computationally-efficient formulae are discussed that yield closed-loop characteristic polynomial coefficients with explicit feedback gain dependence. Then it is shown how the closed-loop characteristic polynomial is associated with the transfer function matrix of the open-loop system. Finally, the results obtained are interpreted graph-theoretically.