FedHC: Federated Graph Clustering with Structure Missing via Hypergraph Contexts

Federated graph-level clustering aims to group decentralized graph data without sharing private graphs. Existing methods usually summarize client knowledge with graph embeddings, cluster prototypes, or pairwise relations. However, they often assume complete graph structures, while real federated data may suffer from structure missing. Directly clustering such graphs can produce unreliable graph representations and biased prototypes, which further affects global clustering. To address this problem, we propose FedHC, a federated graph clustering method that uses hypergraph contexts for structure recovery. On each client, FedHC first builds a graph-instance hypergraph from locally observed graphs, where each hyperedge connects graphs with similar representations and structural patterns. The resulting local hypergraph contexts are used to repair damaged graph structures and obtain more reliable graph representations, and are further summarized into compact context prototypes. The server then builds a prototype hypergraph to integrate related contexts across clients and forms global hypergraph priors, which are distributed back to clients to further guide local structure recovery and clustering. Through this design, FedHC can better adapt to structure missing by exploiting both client-specific structural patterns and cross-client shared structural information within the federated learning process. Experiments on multiple graph benchmark datasets under different structure missing settings show that FedHC outperforms or remains competitive with existing federated graph clustering methods.