  Models of percolation processes on networks currently assume locally
tree-like structures at low densities, and are derived exactly only in the
thermodynamic limit. Finite size effects and the presence of short loops in
real systems however cause a deviation between the empirical percolation
threshold $p_c$ and its model-predicted value $\pi_c$. Here we show the
existence of an empirical linear relation between $p_c$ and $\pi_c$ across a
large number of real and model networks. Such a putatively universal relation
can then be used to correct the estimated value of $\pi_c$. We further show how
to obtain a more precise relation using the concept of the complement graph, by
investigating on the connection between the percolation threshold of a network,
$p_c$, and that of its complement, $\bar{p}_c$.
