  Entropy metrics are nonlinear measures to quantify the complexity of time
series. Among them, permutation entropy is a common metric due to its
robustness and fast computation. Multivariate entropy metrics techniques are
needed to analyse data consisting of more than one time series. To this end, we
present a multivariate permutation entropy, $MPE_G$, using a graph-based
approach.
  Given a multivariate signal, the algorithm $MPE_G$ involves two main steps:
1) we construct an underlying graph G as the Cartesian product of two graphs G1
and G2, where G1 preserves temporal information of each times series together
with G2 that models the relations between different channels, and 2) we
consider the multivariate signal as samples defined on the regular graph G and
apply the recently introduced permutation entropy for graphs.
  Our graph-based approach gives the flexibility to consider diverse types of
cross channel relationships and signals, and it overcomes with the limitations
of current multivariate permutation entropy.
