To rank nodes in quasi-hierarchical networks of social nature, it is necessary to carry out a detailed analysis of the network and evaluate the results obtained according to all the given criteria and identify the most influential nodes. Existing ranking algorithms in the overwhelming majority estimate such networks in general, which does not allow to clearly determine the influence of nodes among themselves. In the course of the study, an analysis of the results of known algorithms for ranking the nodes of HITS, PageRank and compares the obtained data with the expert evaluation of the network. For the effective analysis of quasi-hierarchical networks, the basic algorithm of HITS is modified, which allows to evaluate and rank nodes according to the given criteria (the number of input and output links among themselves), which corresponds to the results of expert evaluation. It is shown that the received method in some cases provides results that correspond to the real social relation, and the indexes of the authorship of the nodes - pre-assigned social roles.