A study on different features of genetic codon analysis can provide us important insights on Amino Acids properties and protein evolution. The natural differentiation between the base positions in the codon, the chemical sorts of bases, purine, pyrimidine and their hydrogen bond number have been playing a pivotal role in the genetic code examination. Taking into consideration of these properties in this manuscript we have defined a distance measure among Amino Acids to study the evolutionary aspects of Amino Acids in protein synthesis. Later, we have applied a graph theoretic approach to study Amino Acids networks and analyzed its different centrality measures. We have also explored the correlation coefficient between centralities measure. Further, we have studied the clustering coefficient and degree distribution as different network parameters.