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Graph neural networks (GNNs) have recently emerged as a promising learning paradigm in learning graph-structured data and have demonstrated wide success across various domains such as recommendation systems, social networks, and electronic design automation (EDA). Like other deep learning (DL) methods, GNNs are being deployed in sophisticated modern hardware systems, as well as dedicated accelerators. However, despite the popularity of GNNs and the recent efforts of bringing GNNs to hardware, the fault tolerance and resilience of GNNs have generally been overlooked. Inspired by the inherent algorithmic resilience of DL methods, this paper conducts, for the first time, a large-scale and empirical study of GNN resilience, aiming to understand the relationship between hardware faults and GNN accuracy. By developing a customized fault injection tool on top of PyTorch, we perform extensive fault injection experiments on various GNN models and application datasets. We observe that the error resilience of GNN models varies by orders of magnitude with respect to different models and application datasets. Further, we explore a low-cost error mitigation mechanism for GNN to enhance its resilience. This GNN resilience study aims to open up new directions and opportunities for future GNN accelerator design and architectural optimization.