Rectangle Counting in Large Bipartite Graphs

Rectangles are the smallest cycles (i.e., cycles of length 4) and most elementary sub-structures in a bipartite graph. Similar to triangle counting in uni-partite graphs, rectangle counting has many important applications where data is modeled as bipartite graphs. However, efficient algorithms for rectangle counting are lacking. We propose three different types of algorithms to cope with different data volumes and the availability of computing resources. We verified the efficiency of our algorithms with experiments on both large real-world and synthetic bipartite graphs.