Graph-directed self-similar sets, also called recurrent self-similar sets or mixed self-similar sets, are a generalization of self-similar sets, which by definition are the unique fixe-points of the operator associated to an iterated function system. A further analysis of these sets (such as, e.g., the computation of the Hausdorff dimension) usually requires some separation condition. Two well-known examples of such a condition are the open set condition (OSC), and the strong open set condition (SOSC). In this paper the author extends an important result of A. Schief [Proc. Am. Math. Soc. 122, No. 1, 111-115 (1994; Zbl 0807.28005)] to mixed self-similar sets: if the matrix describing the mixed self-similar set is irreducible, than the OSC and the SOSC are equivalent. He also gives an example to show that this will not hold in general for mixed self-similar sets.