  The past decade highlighted the usefulness of social network simulations that
run on k-regular, n-size, connected graphs. These can be seen as small-scale
models of human social networks of large societies. By narrowing down onto
k-regular graphs, the degree variation can be eliminated from the research
question, which allows a focus on the isolated impact by other variables, for
instance, by the clustering coefficient or the size of the network. This paper
describes the generation of a random graph library that uses a random walk
graph creation algorithm that starts from the "chain of caves", which is the
structure in which the clustering coefficient is at its maximum. This method
finds mid and high clustering coefficient graphs, while Wolfram`s RandomGraph
was useful for finding low ones. The merge of the two samples proved to be
somewhat biased. After eliminating a host of network measures, the paper
focused on mean graph distance as a further variable and created an unbiased
subsample for each size and clustering coefficient bin.
