Reviews: Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology

This paper presents a theoretical analysis of the representational power of graph convolutional network (GCN) models. It is shown that these models are in many cases incapable of learning topological features of the graph such as graph moments, and these shortcomings are used to motivate new GCN architectures combining several propagation rules and incorporating multiple residual connections. The analysis seems to be sound (albeit distant to my area of expertise), and the obtained emprical results seem to support it. I believe that this paper could serve to better improve understanding of GCNs' representational power, and therefore I would vote for (marginal) acceptance. I have a few comments that could be used to improve the work: - In its current form, it is somewhat unclear what "GCN" exactly refers to.