Horizontal visibility graph transfer entropy (HVG-TE): A novel metric to characterize directed connectivity in large-scale brain networks.

We propose a new measure, horizontal visibility graph transfer entropy (HVG-TE), to estimate the direction of information flow between pairs of time series. HVG-TE quantifies the transfer entropy between the degree sequences of horizontal visibility graphs derived from original time series. Twenty-one Rössler attractors unidirectionally coupled in the posterior-to-anterior direction were used to simulate 21-channel Electroencephalography (EEG) brain networks and validate the performance of the HVG-TE. We showed that the HVG-TE is robust to different levels of coupling strengths between the coupled Rössler attractors, a wide range of time delays, different sample sizes, the effects of noise and linear mixing, and the choice of reference for EEG data. We also applied HVG-TE to EEG data in 20 healthy controls and compared its performance to a recently introduces phase-based TE measure (PTE). We found that compared with PTE, HVG-TE consistently detected stronger posterior-to-anterior information flow patterns in the alpha-band (8-13Hz) EEG brain networks for three different references. Moreover, in contrast to PTE, HVG-TE does not require an assumption on the periodicity of input signals, therefore it can be more widely applicable, even for non-periodic signals. This study shows that the HVG-TE is a directed connectivity measure to characterise the direction of information flow in large-scale brain networks.