Self-stabilizing algorithms are an important because of their robustness and guaranteed convergence. Starting from any arbitrary state, a self-stabilizing algorithm is guaranteed to converge to a legitimate state.Those algorithms are not directly amenable to solving distributed graph processing problems when performance and scalability are important. In this paper, we show the "Abstract Graph Machine" (AGM) model that can be used to convert self-stabilizing algorithms into forms suitable for distributed graph processing. An AGM is a mathematical model of parallel computation on graphs that adds work dependency and ordering to self-stabilizing algorithms. Using the AGM model we show that some of the existing distributed Single Source Shortest Path (SSSP) algorithms are actually specializations of self-stabilizing SSSP. We extend the AGM model to apply more fine-grained orderings at different spatial levels to derive additional scalable variants of SSSP algorithms, essentially enabling the algorithm to be generated for a specific target architecture. Experimental results show that this approach can generate new algorithmic variants that out-perform standard distributed algorithms for SSSP.