The purpose of this paper is to propose a method for reconstructing the weights of a directed weighted signed graph in the absence of observable and measurable variables. An algorithm is proposed that can exactly reconstruct graph weights from one conditional principal eigenvector and a topological pattern of the graph adjacency matrix. The proposed reconstruction algorithm takes into account an important feature of the graph adjacency matrix – the direction of the principal eigenvector to the target vertex (by response). This approach makes it possible to determine the correct solution from a set of fuzzy collinear vectors in the solution space. By integrating the graph spectrum and the efficient control model into a combinatorial optimization problem, we have shown how to achieve a complete reconstruction of the graph weights with acceptable accuracy. We reconstruct the adjacency matrix weights using our approach and compare them with the given graph. The comparison is based on the following global and local graph parameters: the spectrum itself, the similarity coefficients for the reconstructed matrix and the response and control vectors.