  Temporal networks model how the interaction between elements in a complex
system evolve over time. Just like complex systems display collective dynamics,
here we interpret temporal networks as trajectories performing a collective
motion in graph space, following a latent graph dynamical system. Under this
paradigm, we propose a way to measure how the network pulsates and collectively
fluctuates over time and space. To this aim, we extend the notion of linear
correlations function to the case of sequences of network snapshots, i.e. a
network trajectory. We construct stochastic and deterministic graph dynamical
systems and show that the emergent collective correlations are well captured by
simple measures, and illustrate how these patterns are revealed in empirical
networks arising in different domains.
