Neighbourhood-Based Methods for Cohesive Subgraph Mining in Hypergraphs Hyewon Kim (Computer Science and Engineering) Ulsan National Institute of Science and Technology

Abstract

A hypergraph is a powerful tool for modelling higher-order interactions in modern data-rich systems, including online platforms, social networks, and biological systems. By allowing hyperedges to connect multiple entities simultaneously, hypergraphs naturally capture group-based interactions that unipartite graphs cannot represent effectively. Cohesive subgraph mining is vital in hypergraph analysis. While existing studies have predominantly focused on individual node engagement, they often fail to capture the relational aspects among nodes. To address this, neighbourhood-based models have been proposed; however, these models typically consider only the number of neighbours. Thus, even if a node is involved in a single large hyperedge, it may be incorrectly identified as part of a cohesive group. Nonetheless, prior research across various domains suggests that connections involving multiple shared hyperedges are more meaningful, whereas large hyperedges tend to indicate weaker interactions and less meaningful connections. In this thesis, we aim to move beyond simple neighbour counts by identifying cohesive groups that reflect stronger connectivity based on interaction strength. Our approach incorporates the structural characteristics of hypergraphs, thereby laying a foundation for neighbourhood-based hypergraph analysis. The first model, (k,g)-core, defines cohesion based on frequent co-occurrence between node pairs. Rather than focusing solely on connectivity, it identifies subhypergraphs where each node repeatedly shares hyperedges with a sufficient number of neighbours, capturing strong and consistent collaborative patterns. We design a memory-efficient peeling algorithm and a bucket-based core decomposition algorithm that quantifies the structural significance of each node. A parallel implementation further enhances scalability on large-scale hypergraphs. We demonstrate the practical utility and scalability of our method through extensive experiments on both real-world and synthetic datasets. The second model, (k,g, p)-core, extends co-occurrence-based cohesiveness by incorporating the level of participation of nodes within hyperedges. It introduces a node participation ratio to ensure that nodes not only co-occur frequently but also contribute significantly to the hyperedges in which they appear. This allows the model to better distinguish genuinely cohesive groups from those formed by incidental or weak interactions. To support this, we develop a high-performance algorithm with pruning strategies and a lazy update mechanism, significantly improving computational efficiency. We validate its scalability and effectiveness through experiments on real-world and synthetic datasets. The third model, (k,s)-core, introduces a strength-based measure that downweights the influence of large hyperedges. This approach prioritises smaller-scale interactions, facilitating the discovery of stable and cohesive subhypergraphs that reflect meaningful structural patterns. Experimental results confirm the robustness and effectiveness of the model, particularly in scenarios sensitive to hyperedge size.