With the development of graph kernels and graph representation learning, many superior methods have been proposed to handle scalability and oversmoothing issues on graph structure learning. However, most of those strategies are designed based on practical experience rather than theoretical analysis. In this paper, we use a particular dummy node connecting to all existing vertices without affecting original vertex and edge properties. We further prove that such the dummy node can help build an efficient monomorphic edge-to-vertex transform and an epimorphic inverse to recover the original graph back. It also indicates that adding dummy nodes can preserve local and global structures for better graph representation learning. We extend graph kernels and graph neural networks with dummy nodes and conduct experiments on graph classification and subgraph isomorphism matching tasks. Empirical results demonstrate that taking graphs with dummy nodes as input significantly boosts graph structure learning, and using their edge-to-vertex graphs can also achieve similar results. We also discuss the gain of expressive power from the dummy in neural networks.

本文介绍了一种在图形学习中添加虚拟节点的方法，证明此方法可帮助构建有效的同形边到顶点转换和一个保持全局和局部结构的更好的图表示学习，实验证明将具有虚拟节点的图形作为输入可显著提升图形结构学习。

增强虚拟节点在图结构学习中的作用