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 metrics for a large graph or a large set of graphs due to the combinatorial nature of the problem. Despite recent efforts in counting triangles (a 3-node graphlet) 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 fast sampling methods and unbiased estimators of graphlet counts, but also derive simple yet exact formulas for the variances of the estimators which is 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.
|Number of pages
|IEEE Transactions on Knowledge and Data Engineering
|Published - Sep 26 2017
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors wish to thank the anonymous reviewers for their helpful feedback. In addition, the authors also wish to thank Mr. Yiyan Qi and Miss Xiaotong Ren for discussions. This work was supported in part by Army Research Office Contract W911NF-12-1-0385, and ARL under Cooperative Agreement W911NF-09-2-0053. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied of the ARL, or the U.S. Government. The research presented in this paper is supported in part by National Natural Science Foundation of China (U1301254, 61603290, 61602371), the Ministry of Education & China Mobile Research Fund (MCM20160311), the Natural Science Foundation of Jiangsu Province (SBK2014021758), 111 International Collaboration Program of China, the Prospective Joint Research of Industry-Academia-Research Joint Innovation Funding of Jiangsu Province (BY2014074), Shenzhen Basic Research Grant (JCYJ20160229195940462), China Postdoctoral Science Foundation (2015M582663), Natural Science Basic Research Plan in Shaanxi Province of China (2016JQ6034). Junzhou Zhao is the corresponding author.