Title: How Powerful is Implicit Denoising in Graph Neural Networks. Abstract: Graph Neural Networks (GNNs), which aggregate features from neighbors, are widely used for processing graph-structured data due to their powerful representation learning capabilities. It is generally believed that GNNs can implicitly remove feature noises. However, existing works have not rigorously analyzed the implicit denoising effect in graph neural networks. In this work, we conduct a comprehensive theoretical study and analyze when and why implicit denoising happens in GNNs. Our theoretical analysis suggests that the implicit denoising largely depends on the connectivity and size of the graph, as well as the GNN architectures. Motivated by adversarial machine learning in improving the robustness of neural networks, we propose the adversarial graph signal denoising (AGSD) problem. By solving such a problem, we derive a robust graph convolution, where the smoothness of the node representations and the implicit denoising effect can be enhanced. Extensive empirical evaluations verify our theoretical analyses and the effectiveness of our proposed model.