Butterfly Counting in Bipartite Networks

TL;DR

This paper introduces fast randomized algorithms for accurately estimating the number of butterfly motifs in large bipartite networks, enabling efficient analysis of complex higher-order structures.

Contribution

The paper presents novel randomized algorithms with provable guarantees for counting butterflies in bipartite graphs, significantly improving speed and scalability over existing methods.

Findings

Algorithms achieve accurate estimates within seconds

Effective on networks with trillions of butterflies

Scalable to large real-world bipartite networks

Abstract

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 $2 \times 2$ 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.