  In this paper, we address the problem of dynamic network embedding, that is,
representing the nodes of a dynamic network as evolving vectors within a
low-dimensional space. While the field of static network embedding is wide and
established, the field of dynamic network embedding is comparatively in its
infancy. We propose that a wide class of established static network embedding
methods can be used to produce interpretable and powerful dynamic network
embeddings when they are applied to the dilated unfolded adjacency matrix. We
provide a theoretical guarantee that, regardless of embedding dimension, these
unfolded methods will produce stable embeddings, meaning that nodes with
identical latent behaviour will be exchangeable, regardless of their position
in time or space. We additionally define a hypothesis testing framework which
can be used to evaluate the quality of a dynamic network embedding by testing
for planted structure in simulated networks. Using this, we demonstrate that,
even in trivial cases, unstable methods are often either conservative or encode
incorrect structure. In contrast, we demonstrate that our suite of stable
unfolded methods are not only more interpretable but also more powerful in
comparison to their unstable counterparts.
