  For a $d-$regular random model, we assign to vertices $q-$state spins. From
this model, we define the \emph{empirical co-operate measure}, which enumerates
the number of co-operation between a given couple of spins, and \emph{
empirical spin measure}, which enumerates the number of sites having a given
spin on the $d-$regular random graph model. For these empirical measures we
obtain large deviation principle(LDP) in the weak topology.
