Graph convolution networks (GCNs) are currently mainstream in learning with irregular data. These models rely on message passing and attention mechanisms that capture context and node-to-node relationships. With multi-head attention, GCNs become highly accurate but oversized, and their deployment on cheap devices requires their pruning. However, pruning at high regimes usually leads to topologically inconsistent networks with weak generalization. In this paper, we devise a novel method for lightweight GCN design. Our proposed approach parses and selects subnetworks with the highest magnitudes while guaranteeing their topological consistency. The latter is obtained by selecting only accessible and co-accessible connections which actually contribute in the evaluation of the selected subnetworks. Experiments conducted on the challenging FPHA dataset show the substantial gain of our topologically consistent pruning method especially at very high pruning regimes.