  As graph data size increases, the vast latency and memory consumption during
inference pose a significant challenge to the real-world deployment of Graph
Neural Networks (GNNs). While quantization is a powerful approach to reducing
GNNs complexity, most previous works on GNNs quantization fail to exploit the
unique characteristics of GNNs, suffering from severe accuracy degradation.
Through an in-depth analysis of the topology of GNNs, we observe that the
topology of the graph leads to significant differences between nodes, and most
of the nodes in a graph appear to have a small aggregation value. Motivated by
this, in this paper, we propose the Aggregation-Aware mixed-precision
Quantization ($\rm A^2Q$) for GNNs, where an appropriate bitwidth is
automatically learned and assigned to each node in the graph. To mitigate the
vanishing gradient problem caused by sparse connections between nodes, we
propose a Local Gradient method to serve the quantization error of the node
features as the supervision during training. We also develop a Nearest Neighbor
Strategy to deal with the generalization on unseen graphs. Extensive
experiments on eight public node-level and graph-level datasets demonstrate the
generality and robustness of our proposed method. Compared to the FP32 models,
our method can achieve up to a 18.6x (i.e., 1.70bit) compression ratio with
negligible accuracy degradation. Morever, compared to the state-of-the-art
quantization method, our method can achieve up to 11.4\% and 9.5\% accuracy
improvements on the node-level and graph-level tasks, respectively, and up to
2x speedup on a dedicated hardware accelerator.
