  Graph neural networks have emerged as a powerful tool for graph
representation learning, but their performance heavily relies on abundant
task-specific supervision. To reduce labeling requirement, the "pre-train,
prompt" paradigms have become increasingly common. However, existing study of
prompting on graphs is limited, lacking a universal treatment to appeal to
different downstream tasks. In this paper, we propose GraphPrompt, a novel
pre-training and prompting framework on graphs. GraphPrompt not only unifies
pre-training and downstream tasks into a common task template but also employs
a learnable prompt to assist a downstream task in locating the most relevant
knowledge from the pre-trained model in a task-specific manner. To further
enhance GraphPrompt in these two stages, we extend it into GraphPrompt+ with
two major enhancements. First, we generalize several popular graph pre-training
tasks beyond simple link prediction to broaden the compatibility with our task
template. Second, we propose a more generalized prompt design that incorporates
a series of prompt vectors within every layer of the pre-trained graph encoder,
in order to capitalize on the hierarchical information across different layers
beyond just the readout layer. Finally, we conduct extensive experiments on
five public datasets to evaluate and analyze GraphPrompt and GraphPrompt+.
