Heuristic Conductance-Aware Local Clustering for Heterogeneous Hypergraphs

Graphs are widely used to model complex interactions among entities, yet they struggle to capture higher-order and multi-typed relationships. Hypergraphs overcome this limitation by allowing for edges to connect arbitrary sets of nodes, enabling richer modelling of higher-order semantics. Real-world systems, however, often exhibit heterogeneity in both entities and relations, motivating the need for heterogeneous hypergraphs as a more expressive structure. In this study, we address the problem of local clustering on heterogeneous hypergraphs, where the goal is to identify a semantically meaningful cluster around a given seed node while accounting for type diversity. Existing methods typically ignore node-type information, resulting in clusters with poor semantic coherence. To overcome this, we propose HHLC, a heuristic heterogeneous hyperedge-based local clustering algorithm, guided by a heterogeneity-aware conductance measure that integrates structural connectivity and node-type consistency. HHLC employs type-filtered expansion, cross-type penalties, and low-quality hyperedge pruning to produce interpretable and compact clusters. Comprehensive experiments on synthetic and real-world heterogeneous datasets demonstrate that HHLC consistently outperforms strong baselines across metrics such as conductance, semantic purity, and type diversity. These results highlight the importance of incorporating heterogeneity into hypergraph algorithms and position HHLC as a robust framework for semantically grounded local analysis in complex multi-relational networks.