A graph processing system includes a graph API (Application Program Interface), as executed on a processor of a computer and as capable of implementing any of a plurality of graph operators to express computations of input graph analytics applications. A run-time system, executed by the processor, implements graph operators specified by each graph API function and deploys the implemented graph operators to a selected computing system. A library contains multiple implementations for each graph API function, each implementation predetermined as being optimal for a specific set of conditions met by a graph being processed, for functional capabilities of a specific computing system on which the graph is being processed, and for resources available on that specific computing system.