Create a random graph based on the Degree Distribution and Clustering Coefficient Distribution
You may want to have a look at the block two-level Erdos-Renyi model (BTER). The usual preferential attachment mechanism for generating scale-free networks doesn't capture the clustering coefficient right, and small-world networks aren't scale-free; the BTER model can capture both scale-free and clustering behavior. I think they have some way to make it work for an arbitrary degree distribution (not just scale-free). The link I gave above has code for generating BTER graphs too.