Learning high-level representations for graphs is of great importance for graph analysis tasks. In addition to graph convolution, graph pooling is an important but less explored research area. In particular, most of existing graph pooling techniques do not consider the graph structural information explicitly. We argue that such information is important and develop a novel graph pooling technique, know as the STRUCTPOOL, in this work. We consider the graph pooling as a node clustering problem, which requires the learning of a cluster assignment matrix. We propose to formulate it as a structured prediction problem and employ conditional random fields to capture the relationships among assignments of different nodes. We also generalize our method to incorporate graph topological information in designing the Gibbs energy function. Experimental results on multiple datasets demonstrate the effectiveness of our proposed STRUCTPOOL.
The authors here introduces a novel  graph pooling technique called StructPool that uses the underlying graph’s structural information to behave as a node clustering algorithm and learns a node clustering matrix.
Graph level classification requires learning good graph level representation, especially for  aggregating low level information for high . Recent work in pooling does not take advantage of important structural information of the relationship between different  nodes. Here, the authors formulate  graph pooling as a structured prediction problem, control clique set in the CRFs and use mean filed approximation to calculate assignments. 
A cluster assignment matrix assigns each node in the original graph to a cluster in the new graph. The assignment not only depends on the node features but also on the cluster assignment of the other nodes. The authors therefore draw connection with finding the optimal assignment to minimizing the Gibbs energy. The authors propose to learn clustering assignment via CRF conditioned on the global feature representation of the nodes.
The unary potentials of the cliques are computed used the GCN to measure energy of each node. The novelty in accommodating topology information is in using l hop connectivity based on adjacency A to define pairwise cliques thus building pairwise relationship between pairs of nodes thus allowing the Gibbs energy formulation of the cluster assignment thereby using GCN to also compute this pairwise energy. 
I have  a few questions as below:
I think the authors can better elucidate the motivation for using  the attention matrix over Gaussian kernels to measure pairwise energy in section 3.3; an  empirical experiment for drawing comparison wrt to the computational time and number of feature dimensions on a toy problem seems important. 
How is the computation  of the unary potential and pairwise energy influenced by the connectivity of the graph G for the datasets considered? It would be interesting to see how the pairwise energy, unary energy varies over different layers of GCNs. 
Further, how is the cluster assignment affected by the l-hop connectivity? 
Is there a notion of the minimum value of ‘k’ in the context of convergence?
What happens in case of very different graph features, or structural assumptions where the cliques are not enforced? 
Is there a notion of how the method performs on datasets with a high percentage of isomorphism bias: repeating instances or repeating instances with different labels?
It will be interesting to see a discussion on how the performance varies with respect to the depth of the overall architecture,  positioning of the structpool and some results on how effective they are on  hierarchical features and multiple pooling ops as in architectures such as Graph UNet.
Avoid repetition in 2.2 Related work section and in other sections throughout. Otherwise, the paper is rather well written and has clarity.