  Graph Neural Network (GNN) aggregates the neighborhood of each node into the
node embedding and shows its powerful capability for graph representation
learning. However, most existing GNN variants aggregate the neighborhood
information in a fixed non-injective fashion, which may map different graphs or
nodes to the same embedding, reducing the model expressiveness. We present a
theoretical framework to design a continuous injective set function for
neighborhood aggregation in GNN. Using the framework, we propose expressive GNN
that aggregates the neighborhood of each node with a continuous injective set
function, so that a GNN layer maps similar nodes with similar neighborhoods to
similar embeddings, different nodes to different embeddings and the equivalent
nodes or isomorphic graphs to the same embeddings. Moreover, the proposed
expressive GNN can naturally learn expressive representations for graphs with
continuous node attributes. We validate the proposed expressive GNN (ExpGNN)
for graph classification on multiple benchmark datasets including simple graphs
and attributed graphs. The experimental results demonstrate that our model
achieves state-of-the-art performances on most of the benchmarks.
