  The Waxman random graph is a generalisation of the simple Erd\H{o}s-R\'enyi
or Gilbert random graph. It is useful for modelling physical networks where the
increased cost of longer links means they are less likely to be built, and thus
less numerous than shorter links. The model has been in continuous use for over
two decades with many attempts to select parameters which match real networks.
In most the parameters have been arbitrarily selected, but there are a few
cases where they have been calculated using a formal estimator. However, the
performance of the estimator was not evaluated in any of these cases. This
paper presents both the first evaluation of formal estimators for the
parameters of these graphs, and a new Maximum Likelihood Estimator with $O(n)$
computational time complexity that requires only link lengths as input.
