Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are triangle-based and give a measure of the connectedness of mutual friends. This is often summarized in terms of clustering coefficients, which measure the likelihood that two neighbors of a node are themselves connected. Computing these measures exactly for large-scale networks is prohibitively expensive in both memory and time. However, a recent wedge sampling algorithm has proved successful in efficiently and accurately estimating clustering coefficients. In this paper, we describe how to implement this approach in MapReduce to deal with massive graphs. We show results on publicly-available networks, the largest of which is 132M nodes and 4.7B edges, as well as artificially generated networks (using the Graph500 benchmark), the largest of which has 240M nodes and 8.5B edges. We can estimate the clustering coefficient by degree bin (e.g., we use exponential binning) and the number of triangles per bin, as well as the global clustering coefficient and total number of triangles, in an average of 0.33 seconds per million edges plus overhead (approximately 225 seconds total for our configuration). The technique can also be used to study triangle statistics such as the ratio of the highest and lowest degree, and we highlight differences between social and non-social networks. To the best of our knowledge, these are the largest triangle-based graph computations published to date.
Stevens Institute of Technology（史蒂文斯理工学院）；State Key Laboratory for Novel Software Technology, Nanjing University（南京大学软件新技术国家重点实验室）；Huazhong University of Science and Technology（华中科技大学）；Computational Research Division, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室计算研究部）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Department of Computer Science & Engineering, University of Connecticut（康涅狄格大学计算机科学与工程系）；Department of Electrical Engineering and Computer Science, University of California, Merced（加州大学默塞德分校电气与计算机工程系）
