  When a network is reconstructed from data, two types of errors can occur:
false positive and false negative errors about the presence or absence of
links. In this paper, the vertex degree distribution of the true underlying
network is analytically reconstructed using an iterative procedure. Such
procedure is based on the inferred network and estimates for the probabilities
$\alpha$ and $\beta$ of type I and type II errors, respectively. The iteration
procedure consists of choosing various values for $\alpha$ to perform the
iteration steps of the network reconstruction. For the first step, the standard
value for $\alpha$ of 0.05 can be chosen as an example. The result of this
first step gives a first estimate of the network topology of interest. For the
second iteration step the value for $\alpha$ is adjusted according to the
findings of the first step. This procedure is iterated, ultimately leading to a
reconstruction of the vertex degree distribution tailored to its previously
unknown network topology.

Data Analysis, Statistics and Probability;Physics and Society;Computation