A new systems description method that utilizes graph theory for systems modeling is presented. The new method represents the system in terms of a directed graph, where each system component is represented by a vertex and dependencies between system components are represented by directed edges, also called arcs. The absolute dependence rule is introduced as the criterion for the analysis of a system into the graph representation. Together with the concept of an elementary component of a system, the proposed systems description method is applicable to a wide variety of systems for fault diagnosis, reliability engineering and other system modeling and system architecture design purposes. The application of the new method for fault diagnosis is demonstrated in this paper by developing a novel fault management algorithm, and connections with several other systems description methods are presented.