Complex biological systems are described as a multitude of cell-cell interactions (CCIs). Recent single-cell RNA-sequencing studies focus on CCIs based on ligand-receptor (L-R) gene co-expression but the analytical methods are not appropriate to detect many-to-many CCIs. In this work, we propose scTensor, a novel method for extracting representative triadic relationships (or hypergraphs), which include ligand-expression, receptor-expression, and related L-R pairs. Through extensive studies with simulated and empirical datasets, we have shown that scTensor can detect some hypergraphs that cannot be detected using conventional CCI detection methods, especially when they include many-to-many relationships. scTensor is implemented as a freely available R/Bioconductor package.