Int. J. Adv. Appl. Math. and Mech. 2(3) (2015) 31 - 37 (ISSN: 2347-2529) Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics Graph theoretic approach to analyze amino acid network Research Article Adil Akhtar ∗ , Nisha Gohain Department of Mathematics, Dibrugarh University, Dibrugarh-786004, India Received 11 February 2015; accepted (in revised version) 06 March 2015 Abstract: To understand the evolution process of twenty natural amino acids is one of the most important area of the research in biological networks. In this manuscript we have considered the amino acid networks as a biological network based on amino acids properties. To analyze the faster or slower evolutionary process of the amino acids we have discussedclustering coefficient as a graph theoretic tool. We have also investigated the correlation coefficients between degrees of the amino acids. Finally we discuss degree of distribution of the amino acids. MSC: 92B05 • 05C62 • 05C50 Keywords: Amino acid • Clustering coefficient • Correlation coefficient, • Graph c  2015 IJAAMM all rights reserved. 1. Introduction Now a day in natural and artificial systems networks appear almost everywhere. Amino acids play a central role in cellular metabolism, and organisms need to synthesize most of them. There are 20 different amino acids being found till now that occurs in proteins. Each amino acid is a triplet code of four possible bases. A sequence of three bases forms a unit called codon. A codon specifies one amino acid. The genetic code is a series of codons that spec- ify which amino acids are required to make up specific protein. As there are four bases, this gives us 64 codons. In this manuscript we have analyze amino acid networks through graph theoretic approach. Graph theory is one of the most important parts of mathematics, it is a non-numerical branch of modern mathematics considered part of topology, but also closely related to algebra and matrix theory. Application of the various tools of graph theory in biological networkis more important, which help to easily describe and analyze the relevant structures and which lead to findings of many important aspect of the structures. A biological network is any network that apply in biolog- ical system such as protein-protein interaction (PPI), gene regulatory network, neuronal network etc.Several groups have studied in this field. Kundu [1] discussed that hydrophobic and hydrophilic network satisfy â ˘ AIJsmall world property" within protein. Also he has discussed that hydrophobic network have large average degrees of nodes than the hydrophilic network. Aftabuddin and Kundu discussed about three types of networks within protein and gives some idea about all three types of networks [2]. Newman discussed correlation of degree of centrality and betweenness centrality [3]. Also in Newman, discussed about assortative mixing property in the protein interac- tion networks, neural networks and food webs [4]. He also discussed that the information can be easily transferred through an assortative networks as compared to a disassortative network. Sinha and Bagler observed that average clustering coefficients of long range scales shows good negative correlation with the rate of folding, indicating that clustering of amino acids that participate into long range interaction with slow down folding process [5]. Fell and Wagner considered a graph with metabolites as vertices and edges connecting any two metabolites that appear in the same reaction [6] . They have examined whether metabolites with highest degree may belong to the oldest part of the metabolism. Jeong et al. discussed about the lethality and centrality of the PPI network [7] . Where proteins con- sider as a node and edges defined by direct physical interaction between nodes. They have shown that the deletion ∗ Corresponding author. E-mail address: adil.akhtar19@gmail.com