  The degree distributions of complex networks are usually considered to be
power law. However, it is not the case for a large number of them. We thus
propose a new model able to build random growing networks with (almost) any
wanted degree distribution. The degree distribution can either be theoretical
or extracted from a real-world network. The main idea is to invert the
recurrence equation commonly used to compute the degree distribution in order
to find a convenient attachment function for node connections - commonly chosen
as linear. We compute this attachment function for some classical
distributions, as the power-law, broken power-law, geometric and Poisson
distributions. We also use the model on an undirected version of the Twitter
network, for which the degree distribution has an unusual shape. We finally
show that the divergence of chosen attachment functions is heavily links to the
heavy-tailed property of the obtained degree distributions.
