Efficient processing of graph applications on heterogeneous CPU–GPU systems require effectively harnessing the combined power of both the CPU and GPU devices. This paper presents HyPar, a divide-and-conquer model for processing graph applications on hybrid CPU–GPU systems. Our strategy partitions the given graph across the devices and performs simultaneous independent computations on both the devices. The model provides a simple and generic API, supported with efficient runtime strategies for hybrid executions. The divide-and-conquer model is demonstrated with five graph applications and using experiments with these applications on a heterogeneous system it is shown that our HyPar strategy provides equivalent performance to the state-of-art, optimized CPU-only and GPU-only implementations of the corresponding applications. When compared to the prevalent BSP approach for multi-device executions of graphs, our HyPar method yields 74%–92% average performance improvements.