Discovering Significant Communities on Bipartite Graphs: An Index-Based Approach

Kai Wang, Wenjie Zhang, Ying Zhang, Lu Qin, Yuting Zhang

Abstract: Bipartite graphs are widely used to model relationships between two types of entities. Community search retrieves densely connected subgraphs containing a query vertex, which has been extensively studied on unipartite graphs. However, it remains largely unexplored on bipartite graphs. Moreover, all existing cohesive subgraph models on bipartite graphs only measure the structure cohesiveness while overlooking the edge weight. In this paper, we study the significant ( <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> , <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> )-community search problem on weighted bipartite graphs. Given a query vertex <inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula> , we aim to find the significant ( <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> , <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> )-community <inline-formula><tex-math notation="LaTeX">$\mathcal {R}$</tex-math></inline-formula> of <inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula> which adopts ( <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> , <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> )-core to characterize the engagement level of vertices, and maximizes the minimum edge weight (significance) within <inline-formula><tex-math notation="LaTeX">$\mathcal {R}$</tex-math></inline-formula> . To support fast retrieval of <inline-formula><tex-math notation="LaTeX">$\mathcal {R}$</tex-math></inline-formula> , we first obtain the maximal connected subgraph of ( <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> , <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> )-core containing <inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula> (the ( <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> , <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> )-community), and the search space is limited to this subgraph with a much smaller size than the original graph. A novel index structure is presented to support retrieving the ( <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> , <inline-formula><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> )-community in optimal time. Efficient index maintenance techniques are also proposed to handle dynamic graphs. To further obtain <inline-formula><tex-math notation="LaTeX">$\mathcal {R}$</tex-math></inline-formula> , we develop peeling and expansion algorithms. The experimental results on real graphs validate the effectiveness and efficiency of our proposed techniques.