  Graph Neural Networks (GNNs) have been extensively used in various real-world
applications. However, the predictive uncertainty of GNNs stemming from diverse
sources such as inherent randomness in data and model training errors can lead
to unstable and erroneous predictions. Therefore, identifying, quantifying, and
utilizing uncertainty are essential to enhance the performance of the model for
the downstream tasks as well as the reliability of the GNN predictions. This
survey aims to provide a comprehensive overview of the GNNs from the
perspective of uncertainty with an emphasis on its integration in graph
learning. We compare and summarize existing graph uncertainty theory and
methods, alongside the corresponding downstream tasks. Thereby, we bridge the
gap between theory and practice, meanwhile connecting different GNN
communities. Moreover, our work provides valuable insights into promising
directions in this field.
