CCSS: Towards conductance-based community search with size constraints

Abstract

Size-constrained community search, retrieving a size-bounded high-quality subgraph containing user-specified query vertices, has been extensively studied in graph analysis. However, existing methods mainly focus on the cohesiveness within the community while ignoring its separation from the outside, leading to sub-optimal results. Inspired by this, we adopt the well-known conductance to measure the quality of a community and introduce a novel problem of Conductance-based Community Search with Size Constraints (CCSS). CCSS aims to identify a subgraph with the smallest conductance among all connected subgraphs that contain the query vertex q and have at least l and at most h vertices. We prove that CCSS is NP-hard. To efficiently address CCSS, we first propose a computational framework ISC with two-level loops. In the inner loop, ISC starts from q and iteratively adds vertices based on the predefined score function, obtaining a coarse-grained candidate community. In the outer loop, we design the perturbation strategy to repeatedly execute the inner loop until the quality of the candidate community converges. Then, we propose two heuristic algorithms, ISCCI and ISCCP, to concretely implement the score function and perturbation strategy of ISC, which significantly reduce the computational costs. Finally, empirical results demonstrate the superiorities of our solutions. Our source codes and datasets are available at https://github.com/longlonglin/CCSS.