System-state dynamics and recurrence of temporal networks*

Various empirical networks are regarded to vary over time (i.e., temporal networks) on a timescale of relevant dynamics (e.g., epidemic dynamics) occurring on them. Temporal network data are complex because the structure of the network at each time point is quite often complex already, and such a complex network evolves over time. We propose two methods based on stochastic processes and nonlinear time series analysis to simplify temporal networks with the aim of capturing dynamics of temporal network data. In the first approach, we reduce dynamics of networks into that of a single "system state" that switches over time among a relatively small number of possible states. For example, in temporal contact network data measured in a primary school, we find that one of the two inferred states corresponds to class time and the other state corresponds to lunch time. In the second approach, we extend recurrent plots and recurrent quantification analysis, which is a nonlinear time series analysis method proposed in 1980s in physics community, to the case of temporal networks. Specifically, we collect all instances of recurrence in the sense that the network measured at time t_1 is similar to that at t_2. This information allows us to draw recurrence plots, which one can further quantify. I will demonstrate this method with neural data recorded from individuals with epilepsy and with temporal airport networks. With both methods, we crucially need to measure distances between networks at pairs of time points and use that information to create overviews of temporal networks.