We analyse the geometric instability of embeddings produced by graph neural
networks (GNNs). Existing methods are only applicable for small graphs and lack
context in the graph domain. We propose a simple, efficient and graph-native
Graph Gram Index (GGI) to measure such instability which is invariant to
permutation, orthogonal transformation, translation and order of evaluation.
This allows us to study the varying instability behaviour of GNN embeddings on
large graphs for both node classification and link prediction