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State-of-the-art synchronous graph processing frameworks face both inefficiency and imbalance issues that cause their performance to be suboptimal. These issues include the inefficiency of communication and the imbalanced graph computation/communication costs in an iteration. We propose to replace their conventional two-sided communication model with the one-sided counterpart. Accordingly, we design SHMEMGraph, an efficient and balanced graph processing framework that is formulated across a global memory space and takes advantage of the flexibility and efficiency of one-sided communication for graph processing. Through an efficient one-sided communication channel, SHMEMGraph utilizes the high-performance operations with RDMA while minimizing the resource contention within a computer node. In addition, SHMEMGraph synthesizes a number of optimizations to address both computation imbalance and communication imbalance. By using a graph of 1 billion edges, our evaluation shows that compared to the state-of-the-art Gemini framework, SHMEMGraph achieves an average improvement of 35.5% in terms of job completion time for five representative graph algorithms.