Finding top-r weighted k-wing communities in bipartite graphs

Community search in bipartite graphs is an essential problem extensively studied, which aims at retrieving high-quality communities. And $k$-wing is a cohesive subgraph where butterflies (i.e., (2, 2)-biclique) are connected with each other. However, communities based on $k$-wing do not consider weights of edges. Motivated by this, in this paper, we investigate the problem of finding the top-$r$ weighted $k$-wing communities in weighted bipartite graphs. To solve this problem, we propose two baseline algorithms, Globalsearch and Localsearch. The former tries to get results after finding all communities, while the latter aims to reduce the search space by utilizing a group of subgraphs of increasing size. Inspired by LocalSearch, we propose an offline index WNC-Index to filter out edges that are not in the results. In addition, we prove that butterfly connectivity can be transformed to bloom connectivity, thus the finding of $k$-wings can be accelerated by utilizing blooms. Based on this, we propose an online index BCC-Index, which can improve the key steps in our algorithms. Moreover, these two indexes can be used simultaneously to speed up the query process and reduce the space cost of BCC-Index. Finally, we have conducted extensive experiments on ten real-world datasets. The results demonstrate the efficiency and effectiveness of the proposed algorithms.