Graphlet Decomposition: Framework, Algorithms, and Applications (1506.04322v2)

Abstract: From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a tremendous success and impact in a variety of domains, there has yet to be a fast and efficient approach for computing the frequencies of these subgraph patterns. However, existing methods are not scalable to large networks with millions of nodes and edges, which impedes the application of graphlets to new problems that require large-scale network analysis. To address these problems, we propose a fast, efficient, and parallel algorithm for counting graphlets of size k={3,4}-nodes that take only a fraction of the time to compute when compared with the current methods used. The proposed graphlet counting algorithms leverages a number of proven combinatorial arguments for different graphlets. For each edge, we count a few graphlets, and with these counts along with the combinatorial arguments, we obtain the exact counts of others in constant time. On a large collection of 300+ networks from a variety of domains, our graphlet counting strategies are on average 460x faster than current methods. This brings new opportunities to investigate the use of graphlets on much larger networks and newer applications as we show in the experiments. To the best of our knowledge, this paper provides the largest graphlet computations to date as well as the largest systematic investigation on over 300+ networks from a variety of domains.