  A central question of network science is how functional properties of systems
arise from their structure. For networked dynamical systems, structure is
typically quantified with network measures. A functional property that is of
theoretical and practical interest for oscillatory systems is the stability of
synchrony to localized perturbations. Recently, Graph Neural Networks (GNNs)
have been shown to predict this stability successfully; at the same time,
network measures have struggled to paint a clear picture. Here we collect 46
relevant network measures and find that no small subset can reliably predict
stability. The performance of GNNs can only be matched by combining all network
measures and nodewise machine learning. However, unlike GNNs, this approach
fails to extrapolate from network ensembles to several real power grid
topologies. This suggests that correlations of network measures and function
may be misleading, and that GNNs capture the causal relationship between
structure and stability substantially better.
