  We apply the statistical measure of complexity introduced by Lopez-Ruiz,
Mancini and Calbet to neutron stars structure. Neutron stars is a classical
example where the gravitational field and quantum behavior are combined and
produce a macroscopic dense object. Actually, we continue the recent
application of Sanudo and Pacheco to white dwarfs structure. We concentrate our
study on the connection between complexity and neutron star properties, like
maximum mass and the corresponding radius, applying a specific set of realistic
equation of states. Moreover, the effect of the strength of the gravitational
field on the neutron star structure and consequently on the complexity measure
is also investigated. It is seen that neutron stars, consistent with
astronomical observations so far, are ordered systems (low complexity), which
cannot grow in complexity as their mass increases. This is a result of the
interplay of gravity, the short-range nuclear force and the very short-range
weak interaction.
