This paper describes how directed graphs (digraphs) have been used for evaluating the total efficiency of a complex Plant that has been designed for the combined production of food, heat, cooling, and electrical energy. This task required three basic activities. Firstly, the overall plant scheme was studied in detail in order to identify the elementary blocks, each one having its own efficiency value. Each block corresponded to a single node of the digraph. Secondly, the system had to be considered as a whole. The development of the global scheme required the identification of all the directed arcs that were corresponding to the energy flows. Finally, a new algorithm for the evaluation of the overall efficiency was applied to the resultant digraph. This method allowed us to obtain the solution in algebraic symbolic form, automatically, provided that the digraph arc list was supplied to the developed PC code, together with the flow repartitions. The algorithm is quite robust and could also be used in systems with flow recirculation.