The effect of graphene inclusion in the ex-situ $MgB_2$ was analyzed with the help of resistivity behavior and critical current density studies. Amount of graphene was systematically varied from 0% for pristine sample to 3% by the weight of $MgB_2$. Graphene that is considered as a good source of carbon was found to be intact without any significant carbon doping in $MgB_2$ structure as reveled by XRD measurements. There was no signature of graphene inclusion as far as the superconducting transition is concerned which remained same at 39 K for all the samples. The transition width being sensitive to defect doping remained more or less about 2 K for all the samples showing no variation due to doping. Although there was no change in the superconducting transition or transition width, the graphene doped sample showed noticeable decrease in the overall resistivity behavior with respect to decrease in temperature. The graphene inclusion acted as effective pinning centers which have enhanced the upper critical field of these samples.