We highlight a lack of understanding of the behaviour of Convolutional Graph Neural Networks (GNNs) in various topological contexts. We present 4 experimental studies which counter-intuitively demonstrate that the performance of GNNs is weakly dependent on the topology, sensitive to structural noise and the modality (attributes or edges) of information, and degraded by strong coupling between nodal attributes and structure. We draw on the empirical results to recommend reporting of topological context in GNN evaluation and propose a simple (attribute-structure) decoupling method to improve GNN performance.
The paper presents four experimental set-ups to get a better understanding how the performance of Graph Neural Networks (GNN) depend on topological and/or nodal information.
As the paper is not really in my research area, I would have liked the paper to be a bit more self-contained, but the writing of the paper is generally clear. 
The contributions of the paper are mainly experimental and show different "surprising" aspects about GNNs. I found the experimental results to be interesting, especially those presented in Section 5 about decoupling attribute and topological information. However, I think the presentation may be improved and more information (e.g. about how the experiments were conducted or more plots) should be reported in the main paper or the appendix.
Regarding the experiments, the authors made choices about which subsets of datasets (Table 2) or which subsets of measures (Table 1) to use. It would be nice to explain how those choices are made and if they are well-justified. Otherwise, it feels that the presented experimental results have been hand-picked.
Regarding Section 3, I guess that Figure 1 presents averaged results over datasets or over models. I think it would be important to share the results per datasets or per models, as averaging may hide some key aspects.
On page 3, the third paragraph could be illustrated with some plots. Besides, the its first sentence seems to contradict the last sentence of the paragraph before Section 4. Moreover, the text in the fourth paragraph doesn't seem to fit well Fig. 2b for Amazon computers. Am I misreading this plot?
Regarding Section 4, I think it would have been interesting to report the metrics about the topological features for the perturbed graphs. Are they very different from those for the orignal graphs?
Regarding Section 6, the sentence "In the previous sections, we have demonstrated that GNNs .. are robust to perturbations to it" on page 7 seems to contradict the conclusion of Section 4.
I found the experiments in this section to be less convincing. The edge addition technique seems to be ad-hoc and it is not clear why it would improve the performance or not. For instance, how was the value 6°*density-G chosen?
Overall, although I found some of the experimental results very intriguing, I think the paper may not be ready for publication in its current state.