  Graph Convolutional Networks (GCNs) have been widely studied. The core of
GCNs is the definition of convolution operators on graphs. However, existing
Graph Convolution (GC) operators are mainly defined on adjacency matrix and
node features and generally focus on obtaining effective node embeddings which
cannot be utilized to address the graphs with (high-dimensional) edge features.
To address this problem, by leveraging tensor contraction representation and
tensor product graph diffusion theories, this paper analogously defines an
effective convolution operator on graphs with edge features which is named as
Tensor Product Graph Convolution (TPGC). The proposed TPGC aims to obtain
effective edge embeddings. It provides a complementary model to traditional
graph convolutions (GCs) to address the more general graph data analysis with
both node and edge features. Experimental results on several graph learning
tasks demonstrate the effectiveness of the proposed TPGC.
