Analysis and synthesis of communication network structures according to the determined stability indicators

When solving problems related to the analysis and synthesis of communication networks for stability, a special place is simple and easy to understand indicators, weakly linked to the classical concept of exit probability from a state of health. Such deterministic indicators of stability (connectedness, a couple of connections, linear functional connectivity, the number of spanning trees) allow, albeit very approximately, to solve a complex of tasks related to the assessment of the reliability and survivability complex networks. Due to the rather simple analytical form of a linear functional connectivity for the synthesis of structures, it is possible to use the analytical method presented in the work. In this general formulation for the synthesis of connected graphs is formulated as the maximization of the linear functional connectivity for all possible graphs with a given number of edges, vertices, and with fixed values of their weighting coefficients. In general, the deterministic indicators are characterized by a rather serious drawback, which is manifested in the inability to take into account the peculiarities of the functioning of individual communication lines. In addition, for structures of general type, where the expression of the linear functional is not reduced to an analytical form, the constructiveness of such an indicator of connectivity of structures of communication networks (graphs) is less pronounced. In theoretical studies on structures of general type, the linear functional is weakly correlated with already existing concepts (for example, with edge connectivity). Therefore, despite the fact that it, as an indication of connectivity (reliability), can be used to evaluate any structure, in the study of structures of general type, it is more rational to use such indicators of connectivity, which are still in any way consistent with the principles used in graph theory.