  We study the statistical properties of the generation of random graphs
according the configuration model, where one assigns randomly degrees to nodes.
This model is often used, e.g., for the scale-free degree distribution
~d^gamma. For the efficient variant, where non-feasible edges are rejected and
the construction of a graph continues, there exists a bias, which we calculate
explicitly for a small sample ensemble. We find that this bias does not
disappear with growing system size. This becomes also visible, e.g., for
scale-free graphs when measuring quantities like the graph diameter. Hence, the
efficient generation of general scale-free graphs with a very broad
distribution (gamma <2) remains an open problem.
