Unbiased Library of k-regular, n-sized, Connected, Small Graphs

TL;DR

This paper introduces an unbiased library of small, connected, k-regular graphs with controlled clustering coefficients, generated via a novel random walk algorithm, to facilitate social network simulation studies.

Contribution

It presents a new method for generating an unbiased library of k-regular graphs with specific clustering properties, improving the study of social network variables.

Findings

Generated graphs cover a range of clustering coefficients.

The method produces graphs with controlled mean graph distances.

Unbiased subsamples were created for different sizes and clustering levels.

Abstract

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.