The Theory Graph Modeling and Programming Systems from Module Elements to the Application Areas

The mathematical basics of graph modeling and paradigm programming of applied systems (AS) are presented. The vertices of graph are been the functional elements of the systems and the arcs define the connections between them. The graph is represented by an adjacency and reach ability matrix. A number of graph of program structures and their representation by mathematical operations (unions, connections, differences, etc.) are shown. Given the characteristics of graph structures, complexes, units, and systems created from the modules of the graph. The method of modeling the system on the graph of modules, which describe in the programming languages (LP) and calling them with operations (link, assembling, building, etc.). The standard of configuration (2012) Assembly of heterogeneous software elements in AS of different fields of knowledge is made. Brief descriptions of modern and future programming paradigms for formal theoretical creation of systems from service-components for Internet in the near future are given.