  Graph Neural Networks (GNNs) have achieved promising performance on a wide
range of graph-based tasks. Despite their success, one severe limitation of
GNNs is the over-smoothing issue (indistinguishable representations of nodes in
different classes). In this work, we present a systematic and quantitative
study on the over-smoothing issue of GNNs. First, we introduce two quantitative
metrics, MAD and MADGap, to measure the smoothness and over-smoothness of the
graph nodes representations, respectively. Then, we verify that smoothing is
the nature of GNNs and the critical factor leading to over-smoothness is the
low information-to-noise ratio of the message received by the nodes, which is
partially determined by the graph topology. Finally, we propose two methods to
alleviate the over-smoothing issue from the topological view: (1) MADReg which
adds a MADGap-based regularizer to the training objective;(2) AdaGraph which
optimizes the graph topology based on the model predictions. Extensive
experiments on 7 widely-used graph datasets with 10 typical GNN models show
that the two proposed methods are effective for relieving the over-smoothing
issue, thus improving the performance of various GNN models.
