Current approach to the analysis of optimal subnetwork size $R$ doesn’t take into account correlations, arising from many nodes sampling the same subnetworks, and can be see as an approximation. It is accurate for a small number $N$ of nodes in a network, but gives optimistic estimates for larger values of $N$. The consequence of using the latter is a high rate of block rejection which could affect negatively user experience. The improved analysis will take in to account correlations by building an exact distribution based on the factor graph representation of sampling: