  Spatial-temporal graph models are prevailing for abstracting and modelling
spatial and temporal dependencies. In this work, we ask the following question:
whether and to what extent can we localise spatial-temporal graph models? We
limit our scope to adaptive spatial-temporal graph neural networks (ASTGNNs),
the state-of-the-art model architecture. Our approach to localisation involves
sparsifying the spatial graph adjacency matrices. To this end, we propose
Adaptive Graph Sparsification (AGS), a graph sparsification algorithm which
successfully enables the localisation of ASTGNNs to an extreme extent (fully
localisation). We apply AGS to two distinct ASTGNN architectures and nine
spatial-temporal datasets. Intriguingly, we observe that spatial graphs in
ASTGNNs can be sparsified by over 99.5\% without any decline in test accuracy.
Furthermore, even when ASTGNNs are fully localised, becoming graph-less and
purely temporal, we record no drop in accuracy for the majority of tested
datasets, with only minor accuracy deterioration observed in the remaining
datasets. However, when the partially or fully localised ASTGNNs are
reinitialised and retrained on the same data, there is a considerable and
consistent drop in accuracy. Based on these observations, we reckon that
\textit{(i)} in the tested data, the information provided by the spatial
dependencies is primarily included in the information provided by the temporal
dependencies and, thus, can be essentially ignored for inference; and
\textit{(ii)} although the spatial dependencies provide redundant information,
it is vital for the effective training of ASTGNNs and thus cannot be ignored
during training. Furthermore, the localisation of ASTGNNs holds the potential
to reduce the heavy computation overhead required on large-scale
spatial-temporal data and further enable the distributed deployment of ASTGNNs.
