  Are the embeddings of a graph's degenerate core stable? What happens to the
embeddings of nodes in the degenerate core as we systematically remove
periphery nodes (by repeated peeling off $k$-cores)? We discover three patterns
w.r.t. instability in degenerate-core embeddings across a variety of popular
graph embedding algorithms and datasets. We use regression to quantify the
change point in graph embedding stability. Furthermore, we present the STABLE
algorithm, which takes an existing graph embedding algorithm and makes it
stable. We show the effectiveness of STABLE in terms of making the
degenerate-core embedding stable and still producing state-of-the-art link
prediction performance.
