In this paper, the concept of mn-status, minimum and maximum status of an IFG is defined. The definition of a self median intuitionistic fuzzy graph and the necessary and sufficient conditions for an IFG to be self median are given. Also, we discussed the relationship between self median IFG, self centered IFG and constant IFG. We analyzed the conditions for the IFGs,    and  are to be complete.

status, total status, self median, union and intersection of IFGs.