  Graph neural networks are experiencing a surge of popularity within the
machine learning community due to their ability to adapt to non-Euclidean
domains and instil inductive biases. Despite this, their stability, i.e., their
robustness to small perturbations in the input, is not yet well understood.
Although there exists some results showing the stability of graph neural
networks, most take the form of an upper bound on the magnitude of change due
to a perturbation in the graph topology. However, the change in the graph
topology captured in existing bounds tend not to be expressed in terms of
structural properties, limiting our understanding of the model robustness
properties. In this work, we develop an interpretable upper bound elucidating
that graph neural networks are stable to rewiring between high degree nodes.
This bound and further research in bounds of similar type provide further
understanding of the stability properties of graph neural networks.
