  Edge features contain important information about graphs. However, current
state-of-the-art neural network models designed for graph learning, e.g. graph
convolutional networks (GCN) and graph attention networks (GAT), adequately
utilize edge features, especially multi-dimensional edge features. In this
paper, we build a new framework for a family of new graph neural network models
that can more sufficiently exploit edge features, including those of undirected
or multi-dimensional edges. The proposed framework can consolidate current
graph neural network models; e.g. graph convolutional networks (GCN) and graph
attention networks (GAT). The proposed framework and new models have the
following novelties: First, we propose to use doubly stochastic normalization
of graph edge features instead of the commonly used row or symmetric
normalization approches used in current graph neural networks. Second, we
construct new formulas for the operations in each individual layer so that they
can handle multi-dimensional edge features. Third, for the proposed new
framework, edge features are adaptive across network layers. As a result, our
proposed new framework and new models can exploit a rich source of graph
information. We apply our new models to graph node classification on several
citation networks, whole graph classification, and regression on several
molecular datasets. Compared with the current state-of-the-art methods, i.e.
GCNs and GAT, our models obtain better performance, which testify to the
importance of exploiting edge features in graph neural networks.
