The genetic code is the sequence of nucleotides that determines the amino acid sequence of protein molecules during the process of translation. The term codon is used to denote the universal nucleotide triplet that codes for an amino acid. Identity graph of a group G is a graph where vertex set is the set of all elements of the group and two vertices say a and b in G are adjacent if a.b = e, where e is the identity element of G. In the present study, we have analyzed the Identity graph in the genetic code algebra. In our current study different measures of centrality have been comprehensively discussed. Apart from this investigation, a study on the correlation coefficients between different measures of centrality is carried out in addition to clustering coefficient, degree of distribution as well as skewness.