CLPH: Link Prediction in Complex Hyper Networks Through Centrality Weighted Shared Connections

Abstract Link Prediction (LP) aims to infer missing or future interactions in complex networks by exploiting structural patterns. Although widely applied in social, biological, and recommendation systems, traditional graph based LP methods rely solely on pairwise connections and therefore fail to capture the higher-order relationships that naturally arise in many real-world datasets. Hypergraphs offer a richer representation by allowing hyperedges to connect multiple nodes simultaneously. However, converting hypergraphs into simple graphs an approach commonly used in existing work collapses multi-node interactions and results in substantial information loss. Traditional LP metrics also treat all shared neighbors uniformly, despite the fact that shared neighbors may contribute differently to link formation depending on their structural importance or functional relevance. While centrality weighted LP extensions exist, they remain fundamentally restricted by graph structure and do not leverage higher-order dependencies. To address these limitations, we propose CLPH , a hypergraph based link prediction framework that incorporates hypercentrality to weight shared neighbors according to their structural influence. Experiments on four real-world hypergraphs demonstrate that CLPH achieves consistent improvements in AUPR, F1-score, and Precision. Notably, weighting shared neighbors using hypercentrality yields performance gains of 26%–68% compared to traditional centrality based weighting schemes.