ARCHITECTURAL AND MATHEMATICAL MODELING OF NETWORK STRUCTURE SYSTEMS USING S-HYPERNETWORK THEORY

Abstract

The main concepts of the theory of S-hypernetworks are considered. It is shown that the language of this theory can be used to describe many systems of the network structure with sufficient accuracy to solve the given task. In fact, the analytical formulation of the tasks of analysis and synthesis of the structures of the specified systems is almost a simulation model that can be used to solve the tasks. Accordingly, S-hypernetworks can be named according to the mapping of elements. Obviously, in the same S-hypernetwork, different elements can be displayed simultaneously in different ways. Thus, the dictionary of the theory of hypernetworks can be increased due to the features of the display of hypernetwork elements on the surface and various relationships of the incident branches of the edges of secondary networks. The proposed classification of images will allow to set all kinds of tasks related to the description, analysis and synthesis of networks of various purposes. Generally speaking, as it seems at first glance, the most applications of the theory of hypernetworks and S-hypernetworks probably fall on telecommunications and transport. However, it is already clear that the theory of S-hypernetworks is applicable to the analysis and synthesis of many other network structure systems. Of particular interest are the tasks of analyzing inter-network structural interactions of complex systems of various nature. For ecto-hypernetworks, the study of topological properties, in particular, their flat implementation, is of practical importance. The tasks that arise closely overlap with the tasks of stacking graphs on oriented surfaces. However, the specificity of hypernetworks and, in particular, S - hypernetworks entails new topological tasks in the theory of S - hypernetworks. To understand topological tasks, it is necessary to consider different types of embeddings of secondary networks into primary ones. Examples of mapping graphs of secondary networks into the primary network are given, bearing in mind the practical use of the theory in the description and analysis of real systems of the network structure. Also, for practical purposes, an endo-hypernetwork was considered instead of an ecto-hypernetwork.