Applied Physics and Mathematics Annotation << Back THE PROBLEM OF ROUTE DUPLICATE IN COMMUNICATION NETWORKS YU.YU. TERENTYEVA The article proposes a method for finding the maximum set of shortest vertex-independent paths between vertices of a graph, as well as an analytical proof of the effectiveness of the search in the case of the existence of one backup path. That is, the effectiveness of the developed algorithm has been proven for the case when the maximum number of shortest vertex-independent paths is two. In 100 % of cases, the algorithm finds two routes that back up each other if they exist and thereby solves an extremely pressing problem that often arises in the process of designing and/or modernizing a communication network, as well as during its operation. The scope of application of the method includes procedures for obtaining an assessment of the stability of a communication network, estimating the capacity of a communication direction during channel switching. All these procedures are extremely important in the process of designing and/or upgrading a communication network when solving problems of finding backup paths. The need to develop the proposed method is determined primarily by technical and economic factors associated with the organization of backup routes on communication networks. And it is also dictated by the low efficiency of existing algorithms for finding backup routes, which are based on algorithms for finding the shortest paths between the vertices of the communication network graph. It is shown that the problem of finding backup routes must be searched comprehensively, and not sequentially using an algorithm for finding the shortest path. Because for a communication network, relatively speaking, it is more important to have two non-shortest routes that reserve each other than one shortest one that “kills” two potentially available routes. And building a backup route is a resource-intensive undertaking in the general case for high-dimensional communication networks, so the problem of reserving routes in communication networks is extremely relevant and is discussed in this article. Keywords: communication network, stability, route duplicate, vertex-independent paths. DOI: 10.25791/pfi m.01.2024.1288 Pp. 34-41.