Lyapunov Exponents for Temporal Networks

TL;DR

This paper introduces a novel method to quantify the dynamical instability of temporal networks by estimating their maximum Lyapunov exponent directly from network trajectories, extending nonlinear time-series analysis techniques.

Contribution

It extends traditional nonlinear analysis methods to temporal networks, enabling direct estimation of network Lyapunov exponents from single trajectories, and validates this approach on synthetic models.

Findings

Successfully estimates nMLE for synthetic networks with chaotic dynamics

Demonstrates sensitivity to initial conditions in temporal network trajectories

Provides a new tool for analyzing the stability of complex network systems

Abstract

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.