  Graph neural network (GNN) is effective to model graphs for distributed
representations of nodes and an entire graph. Recently, research on the
expressive power of GNN attracted growing attention. A highly-expressive GNN
has the ability to generate discriminative graph representations. However, in
the end-to-end training process for a certain graph learning task, a
highly-expressive GNN risks generating graph representations overfitting the
training data for the target task, while losing information important for the
model generalization. In this paper, we propose Distribution Preserving GNN
(DP-GNN) - a GNN framework that can improve the generalizability of expressive
GNN models by preserving several kinds of distribution information in graph
representations and node representations. Besides the generalizability, by
applying an expressive GNN backbone, DP-GNN can also have high expressive
power. We evaluate the proposed DP-GNN framework on multiple benchmark datasets
for graph classification tasks. The experimental results demonstrate that our
model achieves state-of-the-art performances.
