Randic Index, Irregularity and Complex Biomolecular Networks

A new formulation of Randic index is carried out as a minimization of a quadratic form which involves the Laplacian matrix of a graph. Using this formulation it is easy to realize that Randic index is useful in defining a new index of irregularity, which is then formulated here. A new context for the study of irregularity of graphs is advanced as a necessity for studying complex (biological) networks. We analyze both Randic and irregularity indices for random networks with Poisson and power-law degree distributions. Then, we analyze the irregularity of 10 protein-protein interaction networks in different organisms ranging from 50 to 3000 nodes. Finally, some sruminations’ about the elegance and applicability of Randic index are remarked.