Mosar: Efficiently Characterizing Both Frequent and Rare Motifs in Large Graphs

Due to high computational costs, exploring motif statistics (such as motif frequencies) of a large graph can be challenging. This is useful for understanding complex networks such as social and biological networks. To address this challenge, many methods explore approximate algorithms using edge/path sampling techniques. However, state-of-the-art methods usually over-sample frequent motifs and under-sample rare motifs, and thus they fail in many real applications such as anomaly detection (i.e., finding rare patterns). Furthermore, it is not feasible to apply existing weighted sampling methods such as stratified sampling to solve this problem, because it is difficult to sample subgraphs from a large graph in a direct manner. In this paper, we observe that rare motifs of most real-world networks have “more edges” than frequent motifs, and motifs with more edges are sampled by random edge sampling with higher probabilities. Based on these two observations, we propose a novel motif sampling method, Mosar, to estimate motif frequencies. In particular, our Mosar method samples frequent and rare motifs with different probabilities, and tends to sample motifs with low frequencies. As a result, the new method greatly reduces the estimation errors of these rare motifs. Finally, we conducted extensive experiments on a variety of real-world datasets with different sizes, and our experimental results show that the Mosar method is two orders of magnitude more accurate than state-of-the-art methods.