MOSS-5: A fast method of approximating counts of 5-node graphlets in large graphs

Counting 3-, 4-, and 5-node graphlets in graphs is important for graph mining applications such as discovering abnormal/ evolution patterns in social and biology networks. In addition, it is recently widely used for computing similarities between graphs and graph classification applications such as protein function prediction and malware detection. However, it is challenging to compute these graphlet counts for a large graph or a large set of graphs due to the combinatorial nature of the problem. Despite recent efforts in counting 3-node and 4-node graphlets, little attention has been paid to characterizing 5-node graphlets. In this paper, we develop a computationally efficient sampling method to estimate 5-node graphlet counts. We not only provide a fast sampling method and unbiased estimators of graphlet counts, but also derive simple yet exact formulas for the variances of the estimators which are of great value in practice-the variances can be used to bound the estimates' errors and determine the smallest necessary sampling budget for a desired accuracy. We conduct experiments on a variety of real-world datasets, and the results show that our method is several orders of magnitude faster than the state-of-the-art methods with the same accuracy.