CS224W Project Milestone Project Title: Community Detection Using Local High-Order Structure

Community detection has be widely studied in the research of network analysis, and there are tens of existing tools and techniques to perform this, such as Fielder community (Fiedler 1973), Personalized PageRank algorithm (Andersen et al. 2006), and so on. Most of the previous works aim at finding the subset of nodes that has less incoming and outgoing edges than the edges within the subsets. However, high-order local structure, a.k.a., motif, may contain more information in community level (Benson et al. 2016), thus might give better result in community detection. Benson et al. (2016) generalized the results on Fielder community to motif level. However, the most commonly used way, as well as the one with best performance, to find community based on edge-level information is the Personalized PageRank algorithm, which can not be directly applied to motif analysis. Thus an interesting question is to generalize the Personalized PageRank algorithm to the motif setting, to compare its performance to the Fielder Community, and edge-level algorithms. In this project, we generalized the Personalized PageRank algorithm from edge level to motif level. This part will be covered in Section 4. Besides working on algorithm, we also generalized the definition of clustering coefficient to its high-order version, to make the edge-level analysis smoothly generalized to motif level. This part will be covered in Section 3.