Discovering critical vertices for reinforcement of large-scale bipartite networks

Bipartite networks model relationships between two types of vertices and are prevalent in real-world applications. The departure of vertices in a bipartite network reduces the connections of other vertices, triggering their departures as well. This may lead to a breakdown of the bipartite network and undermine any downstream applications. Such cascading vertex departure can be captured by \((\alpha ,\beta )\)-core, a cohesive subgraph model on bipartite networks that maintains the minimum engagement levels of vertices. Based on \((\alpha ,\beta )\)-core, we aim to ensure the vertices are highly engaged with the bipartite network from two perspectives. (1) From a pre-emptive perspective, we study the anchored \((\alpha ,\beta )\)-core problem, which aims to maximize the size of the \((\alpha ,\beta )\)-core by including some “anchor” vertices. (2) From a defensive perspective, we study the collapsed \((\alpha ,\beta )\)-core problem, which aims to identify the critical vertices whose departure can lead to the largest shrink of the \((\alpha ,\beta )\)-core. We prove the NP-hardness of these problems and resort to heuristic algorithms that choose the best anchor/collapser iteratively under a filter-verification framework. Filter-stage optimizations are proposed to reduce “dominated” candidates and allow computation-sharing. In the verification stage, we select multiple candidates for improved efficiency. Extensive experiments on 18 real-world datasets and a billion-scale synthetic dataset validate the effectiveness and efficiency of our proposed techniques.