Lyapunov exponents for temporal networks

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network and construct a measure to estimate the network maximum Lyapunov exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low- and high-dimensional chaos and finally discuss potential applications.

Automated summary

By interpreting a temporal network as a trajectory of a latent graph dynamical system, the concept of dynamical instability and a measure to estimate the network maximum Lyapunov exponent (nMLE) is introduced. Nonlinear time-series analysis algorithmic methods are extended to networks to quantify sensitive dependence on initial conditions and estimate the nMLE directly from a single network trajectory. The method is validated for synthetic generative network models displaying low- and high-dimensional chaos, and potential applications are discussed.