2 0 Ju n 20 04 Two complementary representations of a scale - free network

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.