  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
$P(k)\approx k^{-\gamma}$, 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 to a power-law
distribution. Our results indicate that a power-law distribution as
$P(k)\approx k^{-\gamma +1}$ 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 to real networks as metabolic
networks, protein-protein interaction network and World Wide Web.
