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A method has been developed for finding the shortest Hamiltonian path in an arbitrary graph based on the rank approach, which provides high efficiency and a significant reduction in the error in solving the problem of organizing the process of managing multiple transactions and queries when they are implemented in network databases. In many cases, existing solutions do not provide the necessary results in terms of access time and accuracy of the found solution. Using the developed method allows minimizing the idle time of computing devices, reducing the volume and time of data transfer from one device to another, increases overall scalability, minimizes data access time, etc. An important advantage of the proposed method is to reduce the number of elementary operations and the number of vectors being processed the queue of the operations of the request, which leads to a significant reduction in time to implement the procedures for the formation of echer di operations in the requests. Methods of graph theory were used in this paper. The effectiveness of the task solution was evaluated using a systems approach, system analysis and the theory of operations research. Processing of experimental data obtained during the work was carried out in accordance with the provisions of mathematical statistics.