If S is a monoid with G as group of units then we can define the relation ???????? on S as follows; x ???????????? if x = yu for some u ∈ G.A unit regular monoid S is said to be R-strongly unit regular if R = ???????? where R is Green’s equivalence on S. In this paper we generate a weighted directed graph namely W corresponding to the set of idempotents of S and we have studied about the properties of weights associated with the edges of W .