Abstract Graph pooling methods provide mechanisms for structure reduction that are intended to ease the diffusion of context between nodes further in the graph, and that typically leverage community discovery mechanisms or node and edge pruning heuristics. In this paper, we introduce a novel pooling technique which borrows from classical results in graph theory that is non-parametric and generalizes well to graphs of different nature and connectivity patterns. Our pooling method, namedKPlexPool, builds on the concepts of graph covers andk-plexes, i.e. pseudo-cliques where each node can miss up toklinks. The experimental evaluation on benchmarks on molecular and social graph classification shows thatKPlexPoolachieves state of the art performances against both parametric and non-parametric pooling methods in the literature, despite generating pooled graphs based solely on topological information.