A novel coronavirus called SARS-CoV-2 was discovered in Wuhan, China, in December 2019, putting an end to everyone’s daily activities. SARS-ancestry Cov-19's evolutionary position are yet unknown. In this study, we used a unique graph theory approach to determine the evolutionary relationships between two bat coronaviruses believed to be the relatives of 2019-nCoV and SARSCoV and seven known human coronaviruses. The maximum likelihood (ML) method has been used to construct the phylogenetic tree of seven coronaviruses (SARS-CoV, 2019-nCoV, MERS-CoV, HCoV-NL63, HCoV-OC43, HCoV-229E, HCoV-HKU1) and other two coronaviruses (RsSHC014 and RaTG13). Network Merge application embedded in Cytoscape 3.3 is used to merge the entire module graph for a single sequence graph and validate the results of the phylogenetic tree using centrality measures with their correlation. RaTG13 is highly correlated with 2019-nCoV (SARSCoV- 2).The novelty of the work lies in the fact that it is one of the research work that shows the evolutionary relationship of protein sequences using rapidly changing regions, instead of the conserved regions. This new graph theory approach gives 100% accuracy of the evolutionary relationship of nine protein sequences with the biologically established one. This work can be used as a pipeline to accomplish evolutionary studies of protein sequences having adjacent residues with at least one common property.