In this paper, two complexity measures of large systems are proposed and a new algorithm based on the disjoint cut set method is presented to compute the complexity measures efficiently. Since the informational and diagnostic entropies reported in the literature do not reflect the structure of a system, an operational entropy (H-O) and an inoperative entropy (H-I) are proposed in this paper to measure the system complexity incorporating the system structure, In addition, an efficient calculational method is provided, The algorithm is exact since it involves no approximation, easy to understand, and computationally efficient.