On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs

Graph neural networks (GNNs) have been widely used in various graph-related problems such as node classification and graph classification, where the superior performance is mainly established when natural node features are available. However, it is not well understood how GNNs work without natural node features, especially regarding the various ways to construct artificial ones. In this paper, we point out the two types of artificial node features,i.e., positional and structural node features, and provide insights on why each of them is more appropriate for certain tasks,i.e., positional node classification, structural node classification, and graph classification. Extensive experimental results on 10 benchmark datasets validate our insights, thus leading to a practical guideline on the choices between different artificial node features for GNNs on non-attributed graphs. The code is available at https://github.com/zjzijielu/gnn-exp/.Comment: This paper has been accepted to the Sixth International Workshop on Deep Learning on Graphs (DLG-KDD'21) (co-located with KDD'21

Just SLaQ When You Approximate: Accurate Spectral Distances for Web-Scale Graphs

Graph comparison is a fundamental operation in data mining and information retrieval. Due to the combinatorial nature of graphs, it is hard to balance the expressiveness of the similarity measure and its scalability. Spectral analysis provides quintessential tools for studying the multi-scale structure of graphs and is a well-suited foundation for reasoning about differences between graphs. However, computing full spectrum of large graphs is computationally prohibitive; thus, spectral graph comparison methods often rely on rough approximation techniques with weak error guarantees. In this work, we propose SLaQ, an efficient and effective approximation technique for computing spectral distances between graphs with billions of nodes and edges. We derive the corresponding error bounds and demonstrate that accurate computation is possible in time linear in the number of graph edges. In a thorough experimental evaluation, we show that SLaQ outperforms existing methods, oftentimes by several orders of magnitude in approximation accuracy, and maintains comparable performance, allowing to compare million-scale graphs in a matter of minutes on a single machine.Comment: To appear at TheWebConf (WWW) 202