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The native three dimensional structure of a single protein is determined by the physico chemical nature of its constituent amino acids. The twenty different types of amino acids, depending on their physico chemical properties, can be grouped into three major classeshydrophobic, hydrophilic and charged. We have studied the anatomy of the weighted and unweighted networks of hydrophobic, hydrophilic and charged residues separately for a large number of proteins. Our results show that the average degree of the hydrophobic networks has significantly larger value than that of hydrophilic and charged networks. The average degree of the hydrophilic networks is slightly higher than that of charged networks. The average strength of the nodes of hydrophobic networks is nearly equal to that of the charged network; whereas that of hydrophilic networks has smaller value than that of hydrophobic and charged networks. The average strength for each of the three types of networks varies with its degree. The average strength of a node in charged networks increases more sharply than that of the hydrophobic and hydrophilic networks. Each of the three types of networks exhibits the 'small-world' property. Our results further indicate that the all amino acids' networks and hydrophobic networks are of assortative type. While maximum of the hydrophilic and charged networks are of assortative type, few others have the characteristics of disassortative mixing of the nodes. We have further observed that all amino acids' networks and hydrophobic networks bear the signature of hierarchy; whereas the hydrophilic and charged networks do not have any hierarchical signature.

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The information regarding the structure of a single protein is encoded in the network of interacting amino acids. Considering each protein as a weighted and unweighted network of amino acids we have analyzed a total of forty nine protein structures that covers the three branches of life on earth. Our results show that the probability degree distribution of network connectivity follows Poisson's distribution; whereas the probability strength distribution does not follow any known distribution. However, the average strength of amino acid node depends on its degree (k). For some of the proteins, the strength of a node increases linearly with k. On the other hand, for a set of other proteins, although the strength increases linaerly with k for smaller values of k, we have not obtained any clear functional relationship of strength with degree at higher values of k. The results also show that the weight of the amino acid nodes belonging to the highly connected nodes tend to have a higher value. The result that the average clustering coefficient of weighted network is less than that of unweighted network implies that the topological clustering is generated by edges with low weights. The ratio of average clustering coefficients of protein network to that of the corresponding classical random network varies linearly with the number (N) of amino acids of a protein; whereas the ratio of characteristic path lengths varies logarithmically with N. The power law behaviour of clustering coefficients of weighted and unweighted network as a function of degree k indicates that the network has a signature of hierarchical network. It has also been observed that the network is of assortative type