Building a random network with a given expected giant component

In this work we show that given any integer-valued random variable D with finite mean such that \(\mathbb {E}[D]>2\) $\mathbb{E}[D]>2$ and \(\mathbb {P}(D\ge 1)=1\) $\mathbb{P}(D\ge 1)=1$ , it is possible to build a configuration model whose giant component has degree distribution that converges in probability to D and give a way to compute the starting degree distribution to achieve this property.