For solid-state systems it is imperative for the learned representation to capture periodicity. The most prominent approach for graph construction in GNNs is radial cutoff where edges from the local neighbourhood of each vertex are constructed by simply selecting the set of all edges with pairwise Euclidean distances less than a specified cutoff, accounting for lattice vectors in periodic systems. Due to all images of each vertex being considered when constructing these edges within cut-off, periodic invariance w.r.t the unit cell origin is achieved. Nevertheless, as the cut-off is increased the number of vertices enclosed within a sphere scales to O(N 3 ) leading to explosive growth in number of edges. In contrast, employing small radial cut-offs may result in "isolated vertices" for certain structures with no connecting edges, preventing information from travelling to and from the vertex, handicapping thus predictive performance.