Truss Decomposition in Hypergraphs

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Abstract

Truss decomposition is a fundamental approach in graph theory that focuses on uncovering cohesive subgraphs within networks. However, many networks involve groupwise rather than pairwise relationships and are often represented as hypergraphs. Modeling and capturing k-truss in hypergraphs is essential for uncovering tight-knit relationships in such multi-relational networks. In this paper, we tackle the problem of truss decomposition in hypergraph. A hyper 𝑘 -truss is a subgraph in which each node is part of at least 𝑘 hyper-triangles. We first introduce a framework for hypertruss decomposition and determine that the most time-consuming component is counting hyper-triangles. To count all hyper-triangles efficiently, we propose an edge-iterator algorithm. To further reduce redundant computations, we present an improved algorithm that combines edge-iterator and node-iterator techniques to prune nonpromising nodes. Next, to handle common nodes in hypergraphs, we develop a novel prefix forest technique to encode all hyperedges and count triangles within this prefix forest. We also propose several optimization strategies that reorder nodes and hyperedges to improve work balancing. Finally, we conduct extensive experiments on real-world hypergraph datasets, demonstrating the efficiency and effectiveness of our algorithms.