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Randic index, irregularity and complex biomolecular networks

Estrada, Ernesto (2010) Randic index, irregularity and complex biomolecular networks. Acta Chimica Slovenica, 57. pp. 597-603. ISSN 1318-0207

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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.