Fig. 1

Cell–cell interaction (CCI) as a hypergraph (CaH). a Previous scRNA-seq studies have regarded CCIs as graphs, and the corresponding data structure can be expressed as an adjacency matrix (left). In this work, CCIs are regarded as context-aware edges (hypergraphs), and the corresponding data structure is a tensor (right). b The CCI-tensor is generated by users’ scRNA-Seq matrices, cell-type labels, and ligand–receptor (L–R) databases. NTD-2 is used to extract CaHs from the CCI-tensor. c Each CaH(r1,r2) is equal to the outer product of three vectors. \(A_{:r1}^{(1)}\) represents the ligand expression pattern, \(A_{:r2}^{(2)}\) represents the receptor expression pattern, and \(G_{r1,r2,:}\) represents the patterns of related L–R pairs