Graph analytics is the basis for many modern applications, e.g., machine learning and streaming data problems. With an unprecedented increase in data size of many emerging domains such as the social networks, which generate a lot of images and documents, real-time big data processing is crucial. Graph processing on traditional computer architectures faces irregular memory accesses that lead to significant data movements and waste a large amount of energy and time. ReRAM-based Processing-in-memory (PIM) is a novel technology that addresses the memory wall problem. Additionally, it provides a high parallelism level and a significant reduction in energy consumption with negligible leakage power. In this paper, we propose a ReRAM-based PIM architecture, named GraphA, which includes a novel reordering algorithm and mapping data to ReRAM Graph Engines (RGE) that cause RGEs to be used with high utilization. Furthermore, we present a compressed format, a memory layout, and proper graph partitioning for graph traversal to eliminate extra communication and useless computation. Moreover, we investigate the computation patterns of graph processing to find a suitable preprocessing model for the proposed GraphA architecture based on reorganizing classified supernode graphs and offering a runtime execution that fits it. Evaluations of GraphA on various real-world graphs show an average performance enhancement and energy saving of 5.3x and 6.0x, respectively, compared with the state-of-the-art GraphR architecture.