  This paper explores whether graph embedding methods can be used as a tool for
analysing the robustness of power-grids within the framework of network
science. The paper focuses on the strain elevation tension spring embedding
(SETSe) algorithm and compares it to node2vec and Deep Graph Infomax, and the
measures mean edge capacity and line load. These five methods are tested on how
well they can predict the collapse point of the giant component of a network
under random attack. The analysis uses seven power-grid networks, ranging from
14 to 2000 nodes. In total, 3456 load profiles are created for each network by
loading the edges of the network to have a range of tolerances and
concentrating network capacity into fewer edges. One hundred random attack
sequences are generated for each load profile, and the mean number of attacks
required for the giant component to collapse for each profile is recorded. The
relationship between the embedding values for each load profile and the mean
collapse point is then compared across all five methods. It is found that only
SETSe and line load perform well as proxies for robustness with $R^2 = 0.89$
for both measures. When tested on a time series normal operating conditions
line load performs exceptionally well ($R=0.99$). However, the SETSe algorithm
provides valuable qualitative insight into the state of the power-grid by
leveraging its method local smoothing and global weighting of node features to
provide an interpretable geographical embedding. This paper shows that graph
representation algorithms can be used to analyse network properties such as
robustness to cascading failure attacks, even when the network is embedded at
node level.
