  We discuss the use of multivariate Granger causality in presence of redundant
variables: the application of the standard analysis, in this case, leads to
under-estimation of causalities. Using the un-normalized version of the
causality index, we quantitatively develop the notions of redundancy and
synergy in the frame of causality and propose two approaches to group redundant
variables: (i) for a given target, the remaining variables are grouped so as to
maximize the total causality and (ii) the whole set of variables is partitioned
to maximize the sum of the causalities between subsets. We show the application
to a real neurological experiment, aiming to a deeper understanding of the
physiological basis of abnormal neuronal oscillations in the migraine brain.
The outcome by our approach reveals the change in the informational pattern due
to repetitive transcranial magnetic stimulations.
