Efficient Computation of Hyper-triangles on Hypergraphs

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Abstract

Hypergraphs, which use hyperedges to capture groupwise inter-Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world net-recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem of computing hyper-works. In this paper, we study the problem of computing hypertriangles (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 exam-can be adopted to compute hyper-triangles by exhaustively examining hyperedge combinations, they overlook the structural char-ining hyperedge combinations, they overlook the structural characteristics distinguishing different hyper-triangle patterns. Conse-acteristics 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, transi-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 hy-hyper-triangles, and classify hyper-triangle patterns based on hyperwedges. Leveraging this insight, we introduce a two-step frame-perwedges. 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 comput-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. Further-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 experimen-based on different hyper-triangle patterns. Extensive experimental evaluations conducted on 11 real-world datasets validate the effectiveness and efficiency of our proposed techniques.