Title: CTODS: Polynomial-Time Construction of Hypergraphs via Constrained Overlapping Densest Subgraphs for Enhanced Neural Network Performance
Primary area: learning on graphs and other geometries & topologies
Keywords: hypergraphs, hypergraph neural networks, hyperedge generation, overlapping densest subgraphs, node classification, graph representation learning

Abstract: The fundamental challenge of constructing meaningful hyperedges from graph structures has limited the effectiveness of hypergraph neural networks in capturing complex relational patterns. We present CTODS (Constrained Top-$K$ Overlapping Densest Subgraphs), a theoretically grounded polynomial-time algorithm that transforms graphs into hypergraphs by systematically identifying overlapping dense subgraphs as hyperedges. The algorithm achieves computational efficiency with $O(K \cdot m \log n)$ time complexity and $O(n + m)$ space requirements while ensuring connectivity-enforced subgraph discovery through a principled distance function that controls overlap. Our adaptive parameter optimization framework enables robust performance across diverse network topologies, from citation networks to geometric structures. Extensive empirical validation across eight benchmark datasets demonstrates the method's superiority, achieving consistent improvements of 1-3\% over existing approaches on seven datasets. The framework effectively models higher-order interactions that remain inaccessible to traditional pairwise representations, establishing a principled foundation for hypergraph-based machine learning applications across multiple domains.

TL;DR: We propose a novel framework for hypergraph generation using top-𝐾 densest overlapping subgraphs and demonstrate its efficiency in enhancing the performance of hypergraph neural networks for  different graph structures and application domains.