Weighted and unweighted network of amino acids within protein
  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. 
Md. Aftabuddin and Sudip Kundu