Efficient Computation of Hyper-triangles on Hypergraphs

2025-04-03

AI Summary

Efficient enumeration and structural differentiation of hypertriangles—triplets of pairwise fully overlapping hyperedges—in hypergraphs remain challenging. Method: We propose a novel hyperwedge-based framework for modeling formation pathways and classifying hypertriangle patterns. We first uncover the structural mechanism by which hypertriangles are generated via hyperwedge expansion, and establish a pattern-aware taxonomy of four hypertriangle types. Our two-stage enumeration paradigm integrates hyperwedge-driven pruning, pattern-specific counting, and fine-grained clustering coefficient metrics. Results: Evaluated on 11 real-world hypergraphs, our algorithm achieves significant improvements in computational efficiency and pattern recognition accuracy. It supports both exact and approximate counting, as well as multi-dimensional structural characterization, thereby establishing a new paradigm for higher-order structural analysis in hypergraphs.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem of computing hyper-triangles (formed by three fully-connected hyperedges), which is a basic structural unit in hypergraphs. Although existing approaches can be adopted to compute hyper-triangles by exhaustively examining hyperedge combinations, they overlook the structural characteristics distinguishing different hyper-triangle patterns. Consequently, these approaches lack specificity in computing particular hyper-triangle patterns and exhibit low efficiency. In this paper, we unveil a new formation pathway for hyper-triangles, transitioning from hyperedges to hyperwedges before assembling into hyper-triangles, and classify hyper-triangle patterns based on hyperwedges. Leveraging this insight, we introduce a two-step framework to reduce the redundant checking of hyperedge combinations. Under this framework, we propose efficient algorithms for computing a specific pattern of hyper-triangles. Approximate algorithms are also devised to support estimated counting scenarios. Furthermore, we introduce a fine-grained hypergraph clustering coefficient measurement that can reflect diverse properties of hypergraphs based on different hyper-triangle patterns. Extensive experimental evaluations conducted on 11 real-world datasets validate the effectiveness and efficiency of our proposed techniques.

Problem

• Efficient computation of hyper-triangles in hypergraphs
• Classifying hyper-triangle patterns using hyperwedges
• Developing fine-grained hypergraph clustering coefficient measurement

Innovation

• Two-step framework reduces hyperedge combination checks
• Efficient algorithms for specific hyper-triangle patterns
• Fine-grained hypergraph clustering coefficient measurement