A graph processing system includes a graph API (Application Programming Interface), as executed by a processor on a computer, and that includes a plurality of graph operators to create graphs and to execute graph analytic applications on the created graphs, the graph operators supporting a creation and manipulation of multi-dimensional properties of graphs. A run-time system is executed by the processor and implements routines that dynamically adjust a plurality of representations and algorithms to execute sequences of operations on graph data. A library is accessible to the run-time system and stores a specification of calling signatures for the graph operators such that the graph operators can be called from any of various computer programming languages such that top-level algorithms received in an input graph application can be understood in the graph processing system when received in any of the various computer programming languages. Thereby the top-level algorithms written to the graph API are portable across multiple implementations.