Bipartite networks are widely applied to model relationships between two distinct types of entities in various real-world applications. The departure of key nodes can trigger a cascading effect, potentially leading to the collapse of the entire community. Identifying such key nodes to enhance community stability is crucial, a topic well-explored in unipartite networks but largely unexplored in bipartite networks. In this paper, we aim to identify key nodes whose removal results in the smallest \(\varvec{(\alpha , \beta )}\) -core in bipartite networks, and protecting these nodes from being removed can greatly enhance community stability. Formally, given a bipartite graph \(\varvec{G}\) with degree constraints \(\varvec{\alpha }\) and \(\varvec{\beta }\) , and budgets \(\varvec{b_1}\) and \(\varvec{b_2}\) , our goal is to identify \(\varvec{b_1}\) upper and \(\varvec{b_2}\) lower vertices (collapsers) whose removal maximizes the number of non-collapsed vertices (followers) cascading out of the \(\varvec{(\alpha , \beta )}\) -core. We prove the problem is NP-hard and propose a greedy algorithm that identifies the best collapser in each of the \(\varvec{b_1+b_2}\) iterations. Several well-designed pruning strategies are employed to reduce the pool of candidate collapsers and expedite follower computation. Theoretical analysis and extensive empirical evaluations on 12 real-world datasets demonstrate the efficiency and effectiveness of our proposed algorithms.
