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** Description:** A model is considered in the form of a multiply connected graph evaluating the importance of the criteria for selecting alternatives for e-learning development systems. A technique is proposed that allows removing the least significant links between the criteria in the original graph. The method is based on the search and subsequent analysis of all (or selective) relationships, while the change in the configuration vector of the ranked graph serves as an indicator of the importance of communication. The methodology is accompanied by a step-by-step procedure for its implementation, which consists of two stages. At the first stage, on the basis of a dialogue with the expert, a multiply connected (holarchic) graph is formed and its formalized representation is realized in the form of corresponding matrices of contiguity and attainability. Next, the rows and columns of the reachability matrix are analyzed in sequence, and a multilevel (ranked) graph is constructed whose configuration is represented as the corresponding vector. At the second stage of the methodology, the links between the criteria are successively broken (and then restored) and the changes in the initial configuration vector are analyzed, which is considered as an indicator of the importance of the link being analyzed. The initial data can be formed both in an interactive mode, by organizing a dialogue with the expert, and by directly filling the adjacency matrix. The obtained results can be used in related fields, where the problems of finding the maximum path (the inverse traveling salesman problem) arise in a multiply connected weight-valued graph.

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Keywords:
** ranked model, multiply connected graph, evaluation, communication, e- learning, tools, criteria

Bratkevych, V.V. (2018), “Metodyka optymyzatsyy sviazei v kholarkhycheskykh modeliakh otsenyvanyia sredstv razrabotky e-learning” [Methodology of broadcasting of relations in cholarchic models of estimation of development facilities e-learning],