Lyapunov Exponents for Temporal Networks

Caligiuri, Annalisa; Eguiluz, Victor; Di Gaetano, Leonardo; Galla, Tobias; Lacasa, Lucas
Physical Review E 107, 044305 (2023)

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.

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