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. However, the analytical methods are still not mature; such methods cannot detect CCIs and the related L-R pairs simultaneously or also 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 could detect some hypergraphs, which cannot be detected by conventional methods, especially when those CCIs are many-to-many relationships.