Graph Homomorphism Convolution

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 prove that graph homomorphism numbers provide a natural universally invariant (isomorphism invariant) embedding maps which can be used for graph classifications. In practice, by choosing $F$ to have bounded tree-width, we show that the homomorphism method is not only competitive in classification accuracy but also run much faster than other state-of-the-art methods. Finally, based on our theoretical analysis, we propose the Graph Homomorphism Convolution module which has promising performance in the graph classification task.