  Relations between the nuclear symmetry energy coefficient and its density
derivatives are derived. The relations hold for a class of interactions with
quadratic momentum dependence and a power-law density dependence. The
structural connection between the different symmetry energy elements as
obtained seems to be followed by almost all reasonable nuclear energy density
functionals, both relativistic and non-relativistic, suggesting a universality
in the correlation structure. This, coupled with known values of some
well-accepted constants related to nuclear matter, helps in constraining values
of different density derivatives of the nuclear symmetry energy shedding light
on the isovector part of the nuclear interaction.
