Abstract: In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some family of graphs (e.g. paths or non-isomorphic trees). We proved that graph homomorphism numbers provide a natural universally invariant embedding maps which can be used for graph classifications. We also discovered that the graph homomorphism method unifies connectivity preserving methods. In practice, by observing that graph classification datasets often have bounded treewidths, we show that our method is not only competitive in classification accuracy but also run much faster than other state-of-the-art. Finally, based on our theoretical analysis, we propose the Graph Homomorphism Convolution module which has promising performance in the graph classification task.