A system of algorithms for the analysis of systems of different nature, the structure of which is given using graphs of great complexity, is proposed. The analysis consists in checking the connectivity and physical realizability of the system, the structure of which is given by the graph, as well as in checking the absence of non-working loops. The proposed algorithms can be used not only to develop new systems but also to diagnose operating equipment and troubleshooting. The approach to determining the physical realizability of a graph is that first a system of basis cycles is constructed. After that it is determined whether each branch is included in one of them. The operation of the system of algorithms is demonstrated by the example of an electrical system. However, the results obtained can be extended to systems of a different nature, for example, using electromechanical analogies.