  Analyzing changes in network evolution is central to statistical network
inference, as underscored by recent challenges of predicting and distinguishing
pandemic-induced transformations in organizational and communication networks.
We consider a joint network model in which each node has an associated
time-varying low-dimensional latent vector of feature data, and connection
probabilities are functions of these vectors. Under mild assumptions, the
time-varying evolution of the latent vectors exhibits low-dimensional manifold
structure under a suitable notion of distance. This distance can be
approximated by a measure of separation between the observed networks
themselves, and there exist Euclidean representations for underlying network
structure, as characterized by this distance, at any given time. These
Euclidean representations, called Euclidean mirrors, permit the visualization
of network evolution and transform network inference questions such as
change-point and anomaly detection into a classical setting. We illustrate our
methodology with real and synthetic data, and identify change points
corresponding to massive shifts in pandemic policies in a communication network
of a large organization.
