The unification process of Rough sets with Graphs is implemented in phenomenal applications in all the fields of Engineering. With the rapid and exponential increase in the worldwide web, it is necessary to organize the data. The major part of the data like google links, the social networks can be represented in graphs. But in the case of uncertainty, the concepts of classical graph theory cannot handle complex networks. For resolving these issues in 2006 Tong He introduced the concepts of Rough Graphs. In this paper, we have introduced metric dimensions in Rough graphs along with their Mathematical Properties.