Beyond Trivial Edges: A Fractional Approach to Cohesive Subgraph Detection in Hypergraphs
Hyewon Kim, Woocheol Shin, Dahee Kim, Junghoon Kim, Sungsu Lim, Hyunji Jeong
TL;DR
This work tackles cohesive subhypergraph detection in hypergraphs by introducing the $(k,g,p)$-core, which adds a hyperedge fraction constraint to suppress trivial, overly large hyperedges that inflate cohesion. It presents two peeling algorithms, Naïve Peeling Algorithm (NPA) and Advanced Support-based Algorithm with Pruning (ASAP), with ASAP employing a supporting table and lazy updates to dramatically reduce redundant $g$-neighbour computations. The authors provide a reuse strategy for varying $p$, and validate superior performance over the baseline $(k,g)$-core across real-world datasets, achieving substantial runtime savings and yielding more meaningful subhypergraphs. The work contributes a practical, scalable framework for high-order cohesive structure discovery in large hypergraphs, with clear paths for adaptive thresholds and stronger lower-bound techniques in future work.
Abstract
Hypergraphs serve as a powerful tool for modeling complex relationships across domains like social networks, transactions, and recommendation systems. The (k,g)-core model effectively identifies cohesive subgraphs by assessing internal connections and co-occurrence patterns, but it is susceptible to inflated cohesiveness due to trivial hyperedges. To address this, we propose the $(k,g,p)$-core model, which incorporates the relative importance of hyperedges for more accurate subgraph detection. We develop both Naïve and Advanced pruning algorithms, demonstrating through extensive experiments that our approach reduces the execution frequency of costly operations by 51.9% on real-world datasets.