  Transfer entropy is an established method for quantifying directed
statistical dependencies in neuroimaging and complex systems datasets. The
pairwise (or bivariate) transfer entropy from a source to a target node in a
network does not depend solely on the local source-target link weight, but on
the wider network structure that the link is embedded in. This relationship is
studied using a discrete-time linearly-coupled Gaussian model, which allows us
to derive the transfer entropy for each link from the network topology. It is
shown analytically that the dependence on the directed link weight is only a
first approximation, valid for weak coupling. More generally, the transfer
entropy increases with the in-degree of the source and decreases with the
in-degree of the target, indicating an asymmetry of information transfer
between hubs and low-degree nodes. In addition, the transfer entropy is
directly proportional to weighted motif counts involving common parents or
multiple walks from the source to the target, which are more abundant in
networks with a high clustering coefficient than in random networks. Our
findings also apply to Granger causality, which is equivalent to transfer
entropy for Gaussian variables. Moreover, similar empirical results on random
Boolean networks suggest that the dependence of the transfer entropy on the
in-degree extends to nonlinear dynamics.
