Abstract
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like P ( k ) ≈ k - γ , where P ( k ) denotes the frequency of the nodes that are connected to k other nodes. Here we have carried out a study on scale-free networks, where a line graph transformation (i.e., edges in an initial network are transformed into nodes) is applied on a power-law distribution. Our results indicate that a power-law distribution as P ( k ) ≈ k - γ + 1 is found for the transformed network together with a peak for low-degree nodes. In the present work, we show a parametrization of this behaviour and discuss its application on real networks as metabolic networks, protein–protein interaction network and World Wide Web.
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