An active research field is the evaluation of the reliability of a complex network. The most popular methods for such evaluation often use Minimal Paths (MP) or Minimal Cuts (MC) of the network. This paper proposes an algorithmic approach to enumerate MC of the directed network's reliability measures. Another attempt has been made in this paper to provide an answer to the question as to when MP or MC are suitable for evaluating reliability measures. An exhaustive study has been conducted to provide some guidelines in this respect.