MODELS OF GRAPH THEORY AS A TOOL FOR MODELING ORGANIZATIONAL SYSTEMS (CLIQUE PROBLEM)

Abstract

The demand for graph theory methods in modeling the process of managing social and economic systems is primarily due to the convenience of graphical display of complex systems, which simplifies their analysis and understanding. At the same time, such a representation allows analyzing the connections between various elements of social and economic systems, which makes it possible to identify key factors that influence the system under study. The aim of the study is to consider the pos¬sibility of using graph theory as a tool for modeling organizational systems using the example of the clique problem. Methods. To solve the problems, it is proposed to use heuristic algorithms based on the use of experience and intuition. In this case, heuristics are used associated with the selection of elements with the greatest weight or the selection of elements covering the largest number of elements. A set of graph theory problems with an algorithmic connection is shown, that is, based on the algorithms for solving one of them, it is possible to obtain a solution for a number of practically important types of problems. The importance of this circumstance lies in the fact that these problems are NP-complete for solving, for which there are no effective solution algorithms. Results. An approximate scheme of application of graph theory problems as a tool for analysis and optimization of social and economic systems is given, allowing to identify the most important elements of the system, determine their interrelations and assess their impact on the overall structure and functioning. Conclusion. As a basic problem allowing to solve several other practically important problems, it is proposed to use the problem of a clique, the solution of which allows to do this. The main problem in this case is to obtain information about whether the graph obtained at the next step is a clique or not. An answer to this question is given, which greatly simplifies the process of finding a clique, and, therefore, solving a whole complex of problems using the concept of an additional graph.