Randić index, irregularity and complex biomolecular networks.
A new formulation of Randić 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 Randić 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 Randić 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 šruminations' about the elegance and applicability of Randić index are remarked.
Ernesto
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Estrada