Graph theory is widely used to analyze the functional properties and interaction of proteins and DNA. This theory of complex networks plays critical role in molecular biology and population biology. Protein-protein interaction networks carry vital information on the organization of molecular interactions in cellular systems. The identification of protein-protein interactions is an important application in biological network analysis Graph Theory is used to apply genomic analysis and in genetic engineering technique. In this paper application of graph theory in protein –protein interaction and genomics were analyzed.