How one should create an Erdos-Renyi random graph with graph_tool? Equivalently, a “G_n_p" graph?

I think, one could create a graph with -n- vertices and n*p edges and then use the random_rewire function with model=‘erdos’. 

Q1. Can I create the input graph of the random_rewire deterministically and rely on the random_rewire to actually do the shuffling? 

Q2. “Turning on” the edge_sweep option  and the niter is it crucial for the graph’s randomness?

And a small suggestion: given the popularity of this type of model, it might worth an example at the documentation, to “attract” more people. 

All the best,

Helen

PS. 

Small side-question: what is the fastest way to create a graph object with n vertices and m edges (any edges other than parallel and self-loops are allowed).