Task-guided Cross-subgraph Topology Learning for Federated Graph Clustering

Federated graph clustering (FGC) aims to group nodes across distributed subgraphs, where missing cross-subgraph edges and privacy constraints hinder global topology learning and reliable cluster assignment. Existing methods typically recover missing cross-subgraph edges using graph-kernel similarity and then perform clustering on the reconstructed graph. However, this recover-then-cluster paradigm is largely decoupled from the clustering objective, as it lacks a task-aware criterion to evaluate the quality of recovered cross-subgraph edges, leading to inferior clustering performance. To address this issue, we propose Task-guided Cross-subgraph Topology Learning (TCTL), which learns cross-subgraph topology explicitly aligned with the clustering objective by exploiting clustering knowledge from both clients and the server. Specifically, we design a gradient-based edge importance estimation scheme to quantify the importance of candidate cross-subgraph edges by leveraging clustering-oriented gradients from the current global clustering state. We further develop a knowledge-driven edge-weight updating scheme, which adopts server-derived gradient feedback as supervision to iteratively refine edge weights conditioned on client-derived cluster semantics. This iterative process allows the learned topology and clustering state to mutually enhance each other. Extensive experiments on five benchmark datasets demonstrate the effectiveness and superiority of TCTL against its competitors.