Generating random graphs with tunable clustering coefficients

Nidhi Parikh, Lenwood Heath

Abstract

Most real-world networks exhibit a high clustering coefficient—the probability that two neighbors of a node are also neighbors of each other. We propose two algorithms, Conf and Throw, that take triangle and single edge degree sequences as input and generate a random graph with a target clustering coefficient. We analyze them theoretically for the case of a regular graph. Conf generates a random graph with the input degree sequence and the clustering coefficient anticipated from the input. Experimental results match quite well with the anticipated clustering coefficient except for highly dense graphs, in which case the experimental clustering coefficient is higher than the anticipated value. For Throw, the degree sequence and the clustering coefficient of the generated graph varies from the input. However, it maintains the expected degree distribution, and the clustering coefficient of the generated graph can also be predicted using analytical results. Experiments show that, for Throw, the results match quite well with the analytical results. Typically, only information about degree distribution is available. We also propose an algorithm Deg that takes degree sequence and clustering coefficient as input and generates a graph with the same properties. Experiments show results for Deg that are quite similar to those for Conf.