How Transitive Are Real-World Group Interactions? -- Measurement and Reproduction

Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the connections between node pairs sharing a neighbor, and it has extensive applications in various domains. Hypergraphs, an extension of graphs, are designed to represent group relations. However, to the best of our knowledge, there has been no examination regarding the transitivity of real-world group interactions. In this work, we investigate the transitivity of group interactions in real-world hypergraphs. We first suggest intuitive axioms as necessary characteristics of hypergraph transitivity measures. Then, we propose a principled hypergraph transitivity measure HyperTrans, which satisfies all the proposed axioms, with a fast computation algorithm Fast-HyperTrans. After that, we analyze the transitivity patterns in real-world hypergraphs distinguished from those in random hypergraphs. Lastly, we propose a scalable hypergraph generator THera. It reproduces the observed transitivity patterns by leveraging community structures, which are pervasive in real-world hypergraphs. Our code and datasets are available at https://github.com/kswoo97/hypertrans.