  We propose a novel graph pooling operation using cliques as the unit pool. As
this approach is purely topological, rather than featural, it is more readily
interpretable, a better analogue to image coarsening than filtering or pruning
techniques, and entirely nonparametric. The operation is implemented within
graph convolution network (GCN) and GraphSAGE architectures and tested against
standard graph classification benchmarks. In addition, we explore the backwards
compatibility of the pooling to regular graphs, demonstrating competitive
performance when replacing two-by-two pooling in standard convolutional neural
networks (CNNs) with our mechanism.
