  Graph convolutional networks (GCNs) have become prevalent in recommender
system (RS) due to their superiority in modeling collaborative patterns.
Although improving the overall accuracy, GCNs unfortunately amplify popularity
bias -- tail items are less likely to be recommended. This effect prevents the
GCN-based RS from making precise and fair recommendations, decreasing the
effectiveness of recommender systems in the long run.
  In this paper, we investigate how graph convolutions amplify the popularity
bias in RS. Through theoretical analyses, we identify two fundamental factors:
(1) with graph convolution (\textit{i.e.,} neighborhood aggregation), popular
items exert larger influence than tail items on neighbor users, making the
users move towards popular items in the representation space; (2) after
multiple times of graph convolution, popular items would affect more high-order
neighbors and become more influential. The two points make popular items get
closer to almost users and thus being recommended more frequently. To rectify
this, we propose to estimate the amplified effect of popular nodes on each
node's representation, and intervene the effect after each graph convolution.
Specifically, we adopt clustering to discover highly-influential nodes and
estimate the amplification effect of each node, then remove the effect from the
node embeddings at each graph convolution layer. Our method is simple and
generic -- it can be used in the inference stage to correct existing models
rather than training a new model from scratch, and can be applied to various
GCN models. We demonstrate our method on two representative GCN backbones
LightGCN and UltraGCN, verifying its ability in improving the recommendations
of tail items without sacrificing the performance of popular items. Codes are
open-sourced \footnote{https://github.com/MEICRS/DAP}.
