  Random graphs with prescribed degree sequences have been widely used as a
model of complex networks. Comparing an observed network to an ensemble of such
graphs allows one to detect deviations from randomness in network properties.
Here we briefly review two existing methods for the generation of random graphs
with arbitrary degree sequences, which we call the ``switching'' and
``matching'' methods, and present a new method based on the ``go with the
winners'' Monte Carlo method. The matching method may suffer from nonuniform
sampling, while the switching method has no general theoretical bound on its
mixing time. The ``go with the winners'' method has neither of these drawbacks,
but is slow. It can however be used to evaluate the reliability of the other
two methods and, by doing this, we demonstrate that the deviations of the
switching and matching algorithms under realistic conditions are small compared
to the ``go with the winners'' algorithm. Because of its combination of speed
and accuracy we recommend the use of the switching method for most
calculations.
