Peeling Bipartite Networks for Dense Subgraph Discovery

TL;DR

This paper introduces a novel framework and efficient algorithms for discovering dense bipartite subgraphs using the butterfly motif, improving upon co-occurrence based methods in real-world affiliation networks.

Contribution

It proposes a new bipartite subgraph framework based on the butterfly motif and develops peeling algorithms that outperform existing co-occurrence graph methods.

Findings

Identifies denser subgraphs than state-of-the-art algorithms.

Reveals hierarchical relations such as collaborator groups and spammers.

Effective on real-world author-paper and user-product networks.

Abstract

Finding dense bipartite subgraphs and detecting the relations among them is an important problem for affiliation networks that arise in a range of domains, such as social network analysis, word-document clustering, the science of science, internet advertising, and bioinformatics. However, most dense subgraph discovery algorithms are designed for classic, unipartite graphs. Subsequently, studies on affiliation networks are conducted on the co-occurrence graphs (e.g., co-author and co-purchase) that project the bipartite structure to a unipartite structure by connecting two entities if they share an affiliation. Despite their convenience, co-occurrence networks come at a cost of loss of information and an explosion in graph sizes, which limit the quality and the efficiency of solutions. We study the dense subgraph discovery problem on bipartite graphs. We define a framework of bipartite subgraphs based on the butterfly motif (2,2-biclique) to model the dense regions in a hierarchical structure. We introduce efficient peeling algorithms to find the dense subgraphs and build relations among them. We can identify denser structures compared to the state-of-the-art algorithms on co-occurrence graphs in real-world data. Our analyses on an author-paper network and a user-product network yield interesting subgraphs and hierarchical relations such as the groups of collaborators in the same institution and spammers that give fake ratings.