  Topology inference for network systems (NSs) plays a crucial role in many
areas. This paper advocates a causality-based method based on noisy
observations from a single trajectory of a NS, which is represented by the
state-space model with general directed topology. Specifically, we first prove
its close relationships with the ideal Granger estimator for multiple
trajectories and the traditional ordinary least squares (OLS) estimator for a
single trajectory. Along with this line, we analyze the non-asymptotic
inference performance of the proposed method by taking the OLS estimator as a
reference, covering both asymptotically and marginally stable systems. The
derived convergence rates and accuracy results suggest the proposed method has
better performance in addressing potentially correlated observations and
achieves zero inference error asymptotically. Besides, an online/recursive
version of our method is established for efficient computation or time-varying
cases. Extensions on NSs with nonlinear dynamics are also discussed.
Comprehensive tests corroborate the theoretical findings and comparisons with
other algorithms highlight the superiority of the proposed method.
