Balanced Butterfly Counting in Bipartite-Network

TL;DR

This paper introduces a novel method for efficiently counting balanced butterflies in signed bipartite graphs, significantly improving speed and enabling practical analysis of complex relationships in real-world networks.

Contribution

The paper presents a new problem of counting balanced butterflies in signed bipartite graphs and proposes a fast, parallel bucket-based algorithm to solve it.

Findings

Up to 120x faster than baseline algorithms.

Parallel implementation is up to 45x faster.

Demonstrated practical relevance through real-world case study.

Abstract

Bipartite graphs offer a powerful framework for modeling complex relationships between two distinct types of vertices, incorporating probabilistic, temporal, and rating-based information. While the research community has extensively explored various types of bipartite relationships, there has been a notable gap in studying Signed Bipartite Graphs, which capture liking / disliking interactions in real-world networks such as customer-rating-product and senator-vote-bill. Balance butterflies, representing 2 x 2 bicliques, provide crucial insights into antagonistic groups, balance theory, and fraud detection by leveraging the signed information. However, such applications require counting balance butterflies which remains unexplored. In this paper, we propose a new problem: counting balance butterflies in a signed bipartite graph. To address this problem, we adopt state-of-the-art algorithms for butterfly counting, establishing a smart baseline that reduces the time complexity for solving our specific problem. We further introduce a novel bucket approach specifically designed to count balanced butterflies efficiently. We propose a parallelized version of the bucketing approach to enhance performance. Extensive experimental studies on nine real-world datasets demonstrate that our proposed bucket-based algorithm is up to 120x faster over the baseline, and the parallel implementation of the bucket-based algorithm is up to 45x faster over the single core execution. Moreover, a real-world case study showcases the practical application and relevance of counting balanced butterflies.