Efficient (α , β , γ )-Core Search in Bipartite Graphs Based on Bi-Triangles

Chuanyu Zong, Wenyang Li, Mengxiang Wang, Tao Qiu

Abstract: Cohesive subgraph search in bipartite graphs has received much interest since the relationship between two different sets of objects in many applications can be modeled as a bipartite graph, such as (\(\alpha \), \(\beta \))-core, (\(\alpha \), \(\beta )_\tau \)-core, and k-bitruss. However, these models have limitations such as \((\alpha , \beta )\)-core may contain some weak ties, \((\alpha , \beta )_{\tau }\)-core lacks generalizability and k-bitruss is too strict. In this paper, therefore, we introduce a novel subgraph model, denoted as the \((\alpha , \beta , \gamma )\text{- }\)core, strategically leveraging the structural characteristics of bi-triangles. This innovative model effectively mitigates the drawbacks observed in previously discussed approaches. The \((\alpha , \beta , \gamma )\text{- }\)core model imposes a requirement that the upper vertex must have at least \(\alpha \) strong ties and the lower vertex must have at least beta strong ties. Furthermore, we define a strong tie as an edge participating in at least \(\gamma \) bi-triangle structures. To tackle the problem of efficiently searching \((\alpha , \beta , \gamma )\text{- }\)cores in bipartite graphs, firstly, we introduce a fundamental algorithm that identifies it through vertex deletions. Subsequently, to streamline computations and enhance efficiency, we observe that certain vertices can be preemptively removed before the \((\alpha , \beta , \gamma )\text{- }\)core search. This insight prompted the development of a pruning algorithm. Furthermore, to further improve the search efficiency, we designed a specialized index tailored for bi-triangles and edge supports. Finally, we conduct extensive experiments on six real bipartite graphs, which yields two findings: (1) the proposed \((\alpha , \beta , \gamma )\text{- }\)core model excels in capturing critical subgraph structures, and (2) the explored algorithms can effectively search \((\alpha , \beta , \gamma )\text{- }\)core in bipartite graphs.