Correlations of network trajectories

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 functions 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.