Can Graph Neural Networks learn node-level structural features?

Graph Neural Networks (GNNs) have become one of the most widely adopted solutions for graph machine learning (GML) tasks. They perform feature learning on graphs using message passing on the network structure, avoiding the feature engineering step required for traditional tabular approaches for GML tasks. However, it is unclear which structural features GNNs can or cannot easily learn from data, especially for node- and edge-level properties. In this work, we propose a methodology to investigate which structural features GNNs can reconstruct from graph data. We conducted a first experimental analysis on one of the most used benchmarks for GML, considering some of the most well-known node-level features, such as centrality and transitivity measures. The results show that GNNs can easily reconstruct PageRank and in/out-degree centralities. But, surprisingly, GNNs can also learn centrality measures based on shortest path distances. Moreover, they reach quite good performance in learning the local clustering coefficient.