Comparative analysis of protein primary sequences with graph energy

•We calculate the graph energy and Laplacian energy of 20 amino acids.•We propose a graphical representation of proteins with no circuit or degeneracy.•We present the increment of graph energy between two protein sequences.•We develop a new similarities model and analyze four different protein datasets.

We propose in this paper, the graph energy and Laplacian energy of 20 amino acids based on the codons coding the amino acids and apply them to put forward a novel 2-D graphical representation of proteins. The novel graphical representation has no circuit or degeneracy, uniquely represents proteins and allows one to easily and quickly visually observe and inspect similarity/dissimilarity between them. It also leads to two novel protein descriptors, the graph energy of a protein sequence, and the increment of graph energy between two protein sequences. We develop similarities/dissimilarities model and successfully analyze the similarities/dissimilarities of ND5, 36PDs36PDs, 24TFs24TFs and 27AFPs27AFPs with good results consistent with ClustalW even better ones.