Graph-structured data is prevalent in many domains. Despite the widely celebrated success of deep neural networks, their power in graph-structured data is yet to be fully explored. We propose a novel network architecture that incorporates advanced graph structural information. In particular, we leverage discrete graph curvature, which measures how the neighborhoods of a pair of nodes are structurally related. The curvature of an edge (x, y) defines the distance taken to travel from neighbors of x to neighbors of y, compared with the length of edge (x, y). It is a much more descriptive structural measure compared to previously ones that only focus on node specific attributes or limited topological information such as degree. Our curvature graph convolution network outperforms state-of-the-art on various synthetic and real-world graphs, especially the larger and denser ones.
In this paper, the authors proposed a novel graph neural network (GNN).
The proposed model combines discrete Ricci curvature of graph edge with GNN. 
The combination method is simple but effective, which is easy to implement and is compatible with existing GNN models like GCN. 
Experimental results show the potentials of the proposed model to node classification. 
My main concerns include:
1. The complexity of the proposed model should be discussed. For a graph with V nodes and E edges, it seems that the authors need to solve E linear programming problems. The scale of each problem is decided by the number of neighbors per node. For large-scale graphs with dense connections, the scalability of the proposed method will be a problem. When the GCN models are with adaptive pooling layers, the curvature will change with respect to the layers of the model, and the scalability problem may become more serious. 
2. For the graphs with isolated nodes, do we need to calculate the curvature associated with such nodes? If yes, how to calculate?
3. The authors introduce additional parameters to model the weight tau_{xy} from the curvature kappa_{xy}, i.e., Eq. (3.4). I wonder whether we can use kappa_{xy} directly as the weight tau_{xy} or not. It would be nice if the authors can add an experiment for this variant. 
Overall, I think the idea of the proposed method is interesting. Introducing Ricci curvature to GCN is a potential method to take advantage of structural information beyond the adjacency matrix. However, the complexity of the proposed method should be analyzed in-depth.