Title: Graph-Graph Similarity Network. Abstract: Graph classification aims to predict the class label for an entire graph. Recently, Graph Neural Networks (GNNs)-based approaches become an essential strand to learn low-dimensional continuous embeddings of the entire graphs for graph label prediction. While GNNs explicitly aggregate the neighborhood information and implicitly capture the topological structure for graph representation, they ignore the relationships among graphs. In this paper, we propose a Graph-Graph Similarity Network to tackle the graph classification problem by constructing a SuperGraph through learning the relationships among graphs. Each node in the SuperGraph represents an input graph, and the weights of edges denote the similarity between graphs. By this means, the graph classification is then transformed into a classical node classification problem. Specifically, we employ an Adversarial Autoencoder to align embeddings of all the graphs to a same distribution. After the alignment, we design the Graph-Graph Similarity Network to learn the similarity between graphs, which function as the adjacency matrix of the SuperGraph. By running node classification algorithms on the SuperGraph, we can predict the labels of graphs. Experiments on five widely used benchmarks under a fair setting demonstrate the effectiveness of our method.