HyperSearch: Prediction of New Hyperedges through Unconstrained yet Efficient Search

TL;DR

This work tackles hyperedge prediction in hypergraphs by proposing HyperSearch, a search-based method that operates over unconstrained candidate sets. It combines an empirically grounded scoring function—favoring high overlap with observed hyperedges, temporal weighting, and optional node-feature similarity—with a theoretically justified anti-monotonic upper bound to prune the search space efficiently. Through extensive experiments on 10 real-world hypergraphs across five domains, HyperSearch consistently achieves higher predictive accuracy and better scalability than state-of-the-art baselines, while providing ablation and sensitivity analyses to justify each component. The approach enhances the practical prediction of missing or emerging HOIs and is accompanied by an open-source implementation for reproducibility.

Abstract

Higher-order interactions (HOIs) in complex systems, such as scientific collaborations, multi-protein complexes, and multi-user communications, are commonly modeled as hypergraphs, where each hyperedge (i.e., a subset of nodes) represents an HOI among the nodes. Given a hypergraph, hyperedge prediction aims to identify hyperedges that are either missing or likely to form in the future, and it has broad applications, including recommending interest-based social groups, predicting collaborations, and uncovering functional complexes in biological systems. However, the vast search space of hyperedge candidates (i.e., all possible subsets of nodes) poses a significant computational challenge, making naive exhaustive search infeasible. As a result, existing approaches rely on either heuristic sampling to obtain constrained candidate sets or ungrounded assumptions on hypergraph structure to select promising hyperedges. In this work, we propose HyperSearch, a search-based algorithm for hyperedge prediction that efficiently evaluates unconstrained candidate sets, by incorporating two key components: (1) an empirically grounded scoring function derived from observations in real-world hypergraphs and (2) an efficient search mechanism, where we derive and use an anti-monotonic upper bound of the original scoring function (which is not antimonotonic) to prune the search space. This pruning comes with theoretical guarantees, ensuring that discarded candidates are never better than the kept ones w.r.t. the original scoring function. In extensive experiments on 10 real-world hypergraphs across five domains, HyperSearch consistently outperforms state-of-the-art baselines, achieving higher accuracy in predicting new (i.e., not in the training set) hyperedges.

Figures (7)

• Figure 1: Observations. (a) The average proportion of ground-truth new hyperedges with overlap ratios with low threshold ($>0$) is comparable to that of the random ones. However, for high thresholds ($\geq 2/3$, $\geq 3/4$, and $1$), the gaps between ground-truth and random ones become significant, suggesting ground-truth new hyperedges are more likely to substantially overlap with existing hyperedges than random hyperedges are. (b) Structural overlap between hyperedges declines as the time gap increases, suggesting new hyperedges tend to overlap more substantially with recent existing ones than with earlier ones.
• Figure 2: Overview of HyperSearch
• Figure 3: Nodes within a hyperedge have similar features. Ground-truth hyperedges show higher Jaccard similarity between features of node pairs, suggesting new hyperedges tend to form between nodes with similar features.
• Figure 4: Q2. Runtime comparison.HyperSearch achieves lower runtime than deep learning-based methods (shown in green) in most cases. For each dataset, we report the running time of HyperSearch and baselines.
• Figure 5: Q3. Ablation studies.Each component of HyperSearch meaningfully contributes to its predictive performance. HyperSearch consistently achieves superior or comparable accuracy compared to its variants with some component missing.

Theorems & Definitions (4)

• Theorem 1
• proof
• Lemma 1
• proof