On Finding Dense Subgraphs in Bipartite Graphs: Linear Algorithms

Detecting dense subgraphs from large graphs is a core component in many applications, ranging from social networks mining, bioinformatics. In this paper, we focus on mining dense subgraphs in a bipartite graph. The work is motivated by the task of detecting synchronized behavior that can often be formulated as mining a bipartite graph formed by the source nodes (followers, customers) and target nodes (followees, products, etc.) for malicious patterns. We introduce a new restricted biclique problem, Maximal Half Isolated Biclique (MHI Biclique), and show that the problem finds immediate applications in fraud detection. We prove that, unlike many other biclique problems such as the maximum edge biclique problem that are known to be NP-Complete, the MHI Biclique problem admits a linear time solution. We provide a novel algorithm S-tree, and its extension, S-forest, that solves the problem efficiently. We also demonstrate that the algorithms are robust against deliberate camouflaging and other perturbations. Furthermore, our approach can automatically combine and prioritize multiple features, reducing the need for feature engineering while maintaining security against unseen attacks. Extensive experiments on several public and proprietary datasets demonstrate that S-tree/S-forest outperforms strong rivals across all configurations, becoming the new state of the art in fraud detection.