  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.
