SLFM: Semi-Supervised Local Community Detection Based on Hyperbolic Flow Matching

Community detection is a longstanding topic in graph and Web algorithms, and semi-supervised local community detection, identifying the community to which the given user belongs, garners increasing research attention in recent years. While achieving encouraging results, existing solutions often encounter accumulated errors due to the weak supervision in the community expansion process, and are undermined by the initial seed sensitivity that a suboptimal or boundary seed node can easily misguide community generation. To fill these gaps, we propose a fresh generative perspective on hyperbolic space, which recasts this problem as the seed-conditioned sequence generation, and reformulates community generation as a continuous transport of probability distributions in the manifold measure space. In this paper, we present a novel Semi-supervised Local community detection framework based on hyperbolic Flow Matching (SLFM). Specifically, it leverages a geometric-aware Seed Selector that refines initial seeds with hyperbolic angular and radial priors, and a Hyperbolic Flow Transporter that learns a vector field to map a source distribution to a target community distribution, generating a robust set of anchors. Finally, a Community Expander is introduced to utilize these anchors as surrogate supervision to effectively recover the full community. Experimental results on four real-world datasets demonstrate that SLFM significantly outperforms existing methods in both local and global semi-supervised settings.