Paper:
Over-fitting and over-smoothing are two main obstacles of developing deep Graph Convolutional Networks (GCNs) for node classification. In particular, over-fitting weakens the generalization ability on small dataset, while over-smoothing impedes model training by isolating output representations from the input features with the increase in network depth. This paper proposes DropEdge, a novel and flexible technique to alleviate both issues. At its core, DropEdge randomly removes a certain number of edges from the input graph at each training epoch, acting like a data augmenter and also a message passing reducer. Furthermore, we theoretically demonstrate that DropEdge either retards the convergence speed of over-smoothing or relieves the information loss caused by it. More importantly, our DropEdge is a general skill that can be equipped with many other backbone models (e.g. GCN, ResGCN, GraphSAGE, and JKNet) for enhanced performance. Extensive experiments on several benchmarks verify that DropEdge consistently improves the performance on a variety of both shallow and deep GCNs. The effect of DropEdge on preventing over-smoothing is empirically visualized and validated as well. Codes will be made public upon the publication.

Review:
The authors propose a simple but effective strategy that aims to alleviate not only overfitting, but also feature degradation (oversmoothing) in deep graph convolutional networks (GCNs).  Inspired by dropout in traditional MLPs and convnets, the authors clearly motivate their contribution in terms of alleviating both overfitting and oversmoothing, which are problems established both in previous literature as well as validated empirically by the authors. Ultimately, the authors provide solid empirical evidence that, while a bit heuristic, their method is effective at alleviating at least partially the issues of overfitting and oversmoothing.
I vote weak-accept in light of convincing empirical results, some theoretical exploration of the method's properties, but limited novelty.
Pros:
Simple, intuitive method
Draws from existing literature relating to dropout-like methods
Little computational overhead
Solid experimental justification
Some theoretical support for the method
Cons:
Method is somewhat heuristic
Mitigates, rather than solves, the issue of oversmoothing
Limited novelty (straightforward extension of dropout to graphs edges)
Unclear why dropping edges is "valid" augmentation
Followup-questions/areas for improving score:
It would be nice to have a principled way of choosing the dropout proportion; 0.8 is chosen somewhat arbitrarily by the authors (presumably because it generally performed well). There is at least a nice interpretation of choosing 0.5 for the dropout proportion in regular dropout (maximum regularization).
As brought up in the comments, edges to drop out to the graph's properties is an interesting direction to explore. While the authors state that they would like to keep the method simple and general, the method is ultimately devised as an adaptation of dropout to graphs, so exploiting graph-specific properties seems reasonable and a potential avenue to further improving performance. 
p2: "First, DropEdge can be considered as a data augmentation technique" Why are these augmentations valid; why should the output of the network be invariant to these augmentations? I would like to see some justification for why the proposed random modification of the graph structure is valid; intuitively, it seems like it might make the learning problem impossible in some cases.
Deeper analysis of the (more interesting, I think) layer-independent regime would be nice. (As a side-note, the name "layer-independent" for this regime is a bit confusing, as the edges dropped out *do* depend on the layer here, whereas in the "layer dependent" regime, edges dropped out do *not* depend on the layer).
Comments:
Figure 1 could probably be re-organized to better highlight the comparison between GCNs with and without DropEdge; consolidating the content into 2 figures instead of 4 might be more easily parsable. Adding figure-specific captions and defining the x axis would also be nice.
Use "reduce" in place of "retard"
p2 " With contending the scalability" improve phrasing
p2 "By recent," -> "Recently,"
p2 "difficulty on" -> "difficulty in"
p2 " deep networks lying" -> "deep networks lies"
p3 "which is a generation of the conclusion" improve phrasing
p3 " disconnected between" -> "disconnected from"
p4 "adjacent matrix" -> "adjacency matrix"
p4 "severer " -> "more severe"
p5 "but has no help" -> "but is no help"
p5 "no touch to the adjacency matrix" -> improve phrasing