We consider the problem of counting motifs in bipartite affiliation networks, such as author-paper, user-product, and actor-movie relations. We focus on counting the number of occurrences of a "butterfly", a complete 2×2 biclique, the simplest cohesive higher-order structure in a bipartite graph. Our main contribution is a suite of randomized algorithms that can quickly approximate the number of butterflies in a graph with a provable guarantee on accuracy. An experimental evaluation on large real-world networks shows that our algorithms return accurate estimates within a few seconds, even for networks with trillions of butterflies and hundreds of millions of edges.
Cite
@article{arxiv.1801.00338,
title = {Butterfly Counting in Bipartite Networks},
author = {Seyed-Vahid Sanei-Mehri and Ahmet Erdem Sariyuce and Srikanta Tirthapura},
journal= {arXiv preprint arXiv:1801.00338},
year = {2018}
}