Finding Introverted Cores in Bipartite Graphs

Kaiyuan Shu, Qi Liang, Haicheng Guo, Fan Zhang, Kai Wang, Long Yuan

Abstract: In this paper, we propose a novel cohesive subgraph model to find introverted communities in bipartite graphs, named \((\alpha , \beta , p)\)-core. It is a maximal subgraph in which every vertex in one part has at least \(\alpha \) neighbors and at least p fraction of its neighbors in the subgraph, and every vertex in the other part has at least \(\beta \) neighbors. Compared to the \((\alpha , \beta )\)-core, the additional requirement on the fraction of neighbors in our model ensures that the vertices are introverted in the subgraph regarding their neighbor sets, e.g., for the \((\alpha , \beta )\)-core of a customer-product network, the shopping interests of the customers inside focus on the products in the subgraph. We propose an O(m) algorithm to compute the \((\alpha , \beta , p)\)-core with given \(\alpha , \beta \) and p. Besides, we introduce an efficient algorithm to decompose a graph by the \((\alpha , \beta , p)\)-core. The experiments on real-world data demonstrate that our model is effective and our proposed algorithms are efficient.