  Graph Neural Networks (GNNs) have risen to prominence in learning
representations for graph structured data. A single GNN layer typically
consists of a feature transformation and a feature aggregation operation. The
former normally uses feed-forward networks to transform features, while the
latter aggregates the transformed features over the graph. Numerous recent
works have proposed GNN models with different designs in the aggregation
operation. In this work, we establish mathematically that the aggregation
processes in a group of representative GNN models including GCN, GAT, PPNP, and
APPNP can be regarded as (approximately) solving a graph denoising problem with
a smoothness assumption. Such a unified view across GNNs not only provides a
new perspective to understand a variety of aggregation operations but also
enables us to develop a unified graph neural network framework UGNN. To
demonstrate its promising potential, we instantiate a novel GNN model,
ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across
nodes. Comprehensive experiments show the effectiveness of ADA-UGNN.
