In order to make up the flaw of low universality of traditional testability inference methods, in the paper, a general purpose testability inference technology was given based on graph theory. A graph theory core was implemented to abstract all testability information from frame model, information flow model, multi-signal flow model, hybrid diagnostic model, Bayesian model and artificial intelligence exchange and service related with all test environments (AI-ESTATE), and melt general-purpose algorithms such as Floyd-Warshall algorithms, fault detection and isolation (FDI) algorithms and high order relation inference algorithms. It has provided a new solution to general-purpose, standard and concurrent testability inference for equipment. Graph theory based general-purpose testability inference technology is shown to be effective and advanced by the example of the testability inference for the certain equipment's signal generation unit.