  The absence of time-reversal symmetry is a fundamental property of many
nonlinear time series. Here, we propose a new set of statistical tests for time
series irreversibility based on standard and horizontal visibility graphs.
Specifically, we statistically compare the distributions of time-directed
variants of the common complex network measures degree and local clustering
coefficient. Our approach does not involve surrogate data and is applicable to
relatively short time series. We demonstrate its performance for paradigmatic
model systems with known time-reversal properties as well as for picking up
signatures of nonlinearity in neuro-physiological data.
