The adoption of graph processing in safety-critical domains has raised serious reliability concerns. A prominent example is the hardware transient faults that can lead to silent data corruption (SDC), severely compromising the reliable execution of graph processing. Even worse, modern graph processing commonly relies on GPUs for acceleration, which aggravates the threat of SDCs due to the higher fault rates in highly integrated GPU platforms. Although redundancy-based techniques effectively mitigate SDCs, they may introduce redundant resources, which can hinder parallelism. This work proposes GraphFT, a lightweight fault-tolerant framework for protecting graph processing against SDCs. Our key insight is that the monotonicity in vertex value updates can be utilized to guide lightweight SDC detection and heuristic SDC recovery in iterative graph processing. Specifically, we observe that faults violating monotonicity are closely associated with severe SDCs. Leveraging the inherent resilience and computational characteristics of graph processing, GraphFT corrects faulty states locally without re-computation, thereby mitigating the effects of severe SDCs. Our evaluation on four iterative graph algorithms shows that GraphFT can mitigate SDCs to between 1.27% and 20% with an average time overhead of 6.79%. Compared to triple modular redundancy methods, GraphFT achieves up to a 14x improvement in SDC mitigating efficiency (i.e., the ratio of SDC mitigation rate to overhead).