Efficient maximum signed biclique and biplex identification in signed bipartite graphs

Renjie Sun, Chen Chen, Xiaoyang Wang, Yanping Wu, Wenjie Zhang, Ying Zhang, Xuemin Lin

Abstract: In the literature, various cohesive subgraph models for bipartite graphs have been proposed for different applications. One important cohesive structure is biclique, where each vertex in one set is completely connected to all vertices in the other set. However, previous studies mainly focus on unsigned bipartite graphs, while signed information naturally exists in real applications, such as trust/distrust and friendship/antagonism. The neglect of signed information may fail to discover the inherent properties of networks. In this paper, we propose a novel model, named signed (k, l)-biclique (SBC), by enforcing constraints over the number of positive and negative connections. Specifically, given a signed bipartite graph and two positive integers k, l, SBC is a biclique, where each vertex has no less than k positive neighbors and no more than l negative neighbors. Considering the strict requirement of biclique, which may limit its application in real scenarios, we further introduce a new model, named signed \((k,l,\theta )\)-biplex (SBP), which relaxes the biclique constraint in SBC with the \(\theta \)-biplex model. We prove the problems of finding the maximum signed (k, l)-biclique (MaxSBC) and the maximum signed \((k,l,\theta )\)-biplex (MaxSBP) are both NP-hard. To solve the two problems, efficient search paradigms are developed accordingly. Moreover, to handle large graphs, targeted optimization strategies are designed for each model, including effective unpromising vertex filtering and unnecessary branch pruning. Finally, comprehensive experiments are conducted on 10 graphs to demonstrate the efficiency and effectiveness of the proposed techniques and models.

External IDs:dblp:journals/vldb/SunCWWZZL25