Generate a random connected graph with a uniform distribution

Are there any C/C++ algorithms / libraries out there that will generate a connected, undirected graph with a uniform distribution? For example, there are 11,117 undirected, connected graphs with 8 vertices. I'd like an algorithm that will randomly generate each of these graphs with probability 1/11117.

(Am I correct that the Erdős-Rényi model does not produce a uniform distribution? http://ift.tt/1zsFQim)