graphenum is a package of software to generate connected simple graphs.
There are 2 implementations:
The Python version is much easier to understand, I hope. The C version is much faster as you expect.
The Python version can generate up to 10 vertices graphs. The C version can generate up to 11 vertices graphs. Both limits mean the realistic running time: in 1 day.
Those who are interested in the algorithm used, consult the document in doc/.
The software is licensed under the 2-clause BSD license. See LICENSE.