  Graph Neural Network (GNN) is a powerful model to learn representations and
make predictions on graph data. Existing efforts on GNN have largely defined
the graph convolution as a weighted sum of the features of the connected nodes
to form the representation of the target node. Nevertheless, the operation of
weighted sum assumes the neighbor nodes are independent of each other, and
ignores the possible interactions between them. When such interactions exist,
such as the co-occurrence of two neighbor nodes is a strong signal of the
target node's characteristics, existing GNN models may fail to capture the
signal. In this work, we argue the importance of modeling the interactions
between neighbor nodes in GNN. We propose a new graph convolution operator,
which augments the weighted sum with pairwise interactions of the
representations of neighbor nodes. We term this framework as Bilinear Graph
Neural Network (BGNN), which improves GNN representation ability with bilinear
interactions between neighbor nodes. In particular, we specify two BGNN models
named BGCN and BGAT, based on the well-known GCN and GAT, respectively.
Empirical results on three public benchmarks of semi-supervised node
classification verify the effectiveness of BGNN -- BGCN (BGAT) outperforms GCN
(GAT) by 1.6% (1.5%) in classification accuracy.Codes are available at:
https://github.com/zhuhm1996/bgnn.
