  One of the fundamental open questions in plasma physics is the role of
non-thermal particles distributions in poorly collisional plasma environments,
a system commonly found throughout the Universe, e.g. the solar wind and the
Earth's magnetosphere correspond to natural plasma physics laboratories in
which turbulent phenomena can be studied. Our study perspective is born from
the method of Horizontal Visibility Graph (HVG) that has been developed in the
last years to analyze time series avoiding the tedium and the high
computational cost that other methods offer. Here we build a complex network
based on directed HVG technique applied to magnetic field fluctuations time
series obtained from Particle In Cell (PIC) simulations of a magnetized
collisionless plasma to distinguish the degree distributions and calculate the
Kullback-Leibler Divergence (KLD) as a measure of relative entropy of data sets
produced by processes that are not in equilibrium. First, we analyze the
connectivity probability distribution for the undirected version of HVG finding
how the Kappa distribution for low values of $\kappa$ tends to be an
uncorrelated time series, while the Maxwell-Boltzmann distribution shows a
correlated stochastic processes behavior. Then, we investigate the degree of
temporary irreversibility of magnetic fluctuations self-generated by the
plasma, comparing the case of a thermal plasma (described by a Maxwell-Botzmann
velocity distribution function) with non-thermal Kappa distributions. We have
shown that the KLD associated to the HVG is able to distinguish the level of
reversibility associated to the thermal equilibrium in the plasma because the
dissipative degree of the system increases as the value of $\kappa$ parameter
decreases and the distribution function departs from the Maxwell-Boltzmann
equilibrium.
