Maximum Balanced ( k , ϵ )-Bitruss Detection in Signed Bipartite Graph

Signed bipartite graphs represent relationships between two sets of entities, including both positive and negative interactions, allowing for a more comprehensive modeling of real-world networks. In this work, we focus on the detection of cohesive subgraphs in signed bipartite graphs by leveraging the concept of balanced butterflies. A balanced butterfly is a cycle of length 4 that is considered stable if it contains an even number of negative edges. We propose a novel model called the balanced ( k , ϵ)-bitruss, which provides a concise representation of cohesive signed bipartite subgraphs while enabling control over density ( k ) and balance (ϵ). We prove that finding the largest balanced ( k , ϵ)-bitruss is NP-hard and cannot be efficiently approximated to a significant extent. Furthermore, we extend the unsigned butterfly counting framework to efficiently compute both balanced and unbalanced butterflies. Based on this technique, we develop two greedy heuristic algorithms: one that prioritizes followers and another that focuses on balanced support ratios. Experimental results demonstrate that the greedy approach based on balanced support ratios outperforms the follower-based approach in terms of both efficiency and effectiveness.