Purpose of the study. The problem of determining the rating of an expert is considered. In this case, the rating will be determined by the results of the last discussion, that is, the assessment of the i-th expert will depend on the assessment that he received as a result of this discussion. Relationships in such a community are proposed to be described using an interaction graph. It is shown that this interaction graph will be described by the Kirchhoff matrix, which has a determinant equal to zero and a rank one less than the dimension of the Kirchhoff matrix. Materials and methods. Thus, to solve the problem posed, it is required to find a solution to a homogeneous system of equations whose matrix is the Kirchhoff matrix. It is proposed to use an algorithm that can be applied without numerous intermediate transformations, but it is required to carry out the operation of inverting the original matrix of a sufficiently large dimension. This appears to be a rather labor intensive operation. That is why it is proposed to use the Tikhonov regularization method, which allows replacing the solution of the original problem with the problem of minimizing the Tikhonov functional. Such a replacement leads to the problem of the complexity of the solution of which is also significant. Therefore, taking into account the property of the problem being solved, when it is necessary to obtain not the absolute value of the rating, but a system of ratings that reflect the relative importance of each expert in relation to each other, an approximate algorithm for solving the problem is proposed when the value of the regularizing parameter is selected during iterations. Results. An example is considered for the case of five experts, the matrix of interaction between the participants of this expert community is given in the form of a table. The above algorithm makes it possible to assess the competence of experts quite accurately and precisely for a specific situation, taking into account the opinion of the entire expert community. Next, we consider the case when there is information about the initial rating of each of the experts. Focusing on the fact that in order to solve the problem it is necessary to find not the absolute value of the rating of each expert, but only the ratio between the ratings, we arrive at an algorithm that allows us to move from a homogeneous system of equations to a heterogeneous one, thereby bypassing the need to invert a large-dimensional matrix. Conclusion. An algorithm for solving the problem of constructing a rating estimate for two cases is considered: there are no initial estimates of the competence of specialists and the case when there is information about the initial rating of each of the experts.
