  We study a recent model of random networks based on the presence of an
intrinsic character of the vertices called fitness. The vertices fitnesses are
drawn from a given probability distribution density. The edges between pair of
vertices are drawn according to a linking probability function depending on the
fitnesses of the two vertices involved. We study here different choices for the
probability distribution densities and the linking functions. We find that,
irrespective of the particular choices, the generation of scale-free networks
is straightforward. We then derive the general conditions under which
scale-free behavior appears. This model could then represent a possible
explanation for the ubiquity and robustness of such structures.
