In this paper, the new method of the determination of entries of the state matrices of the positive one-dimensional systems with delay using multidimensional digraphs theory D⁽ⁿ⁾ has been presented. For the proposed method, parallel computing algorithm was constructed. This algorithm is based on GPGPU (General-Purpose Computing on Graphics Processing Units) computing method to gain needed speed and computational power for such a solution. The proposed method was discussed and illustrated with numerical examples. The proposed solution allows minimal digraphs construction for any positive one-dimensional system with delays, regardless of its complexity.