There may be a large number of algorithms proposed for generating graphs satisfying some common properties (e.g., clustering coefficient, average shortest path length, degree distribution, etc).
My question concerns a specific case: I want to generate a few undirected regular graphs (i.e., every node in these graphs has the same number of neighbors) with different clustering coefficients and average shortest path lengths. More generally, by fixing a degree distribution, I want to generate graphs with different clustering coefficients and average shortest path lengths.
I wonder what are the well-known algorithms for doing this (or in fact, is there any?), and what are the recommended software for the same purpose?