Fig. 1: Hierarchical structures in cell-cell communications.

a A hierarchical clustering of cells. Cell groups at scale 2 are subclusters of cell groups at scale 1. b Hierarchical structures within ligands, receptors, or union of ligands and receptors. (i) In the hierarchy of ligands, all cells express red ligands, some the cells express yellow ligands, and some cells express green ligands, etc. (ii) In the hierarchy of ligand-receptor unions, all cells express either the red ligand or receptor. Within the group of cells expressing the yellow ligand or receptor, there are also cells expressing either the purple ligand or receptor, and blue ligand or receptor. c Hierarchical structures of ligand-receptor interactions. There are four hierarchical relationships of ligand-receptor interactions ligand inclusion, ligand, disjointness, receptor inclusion, and receptor disjointness. d Representations of cell-cell communication between hierarchical clustering of cells based on ligands (left) and receptors (right). The node sizes correspond to the number of cells in the groups, and the edge widths represent interaction strengths. e Tree representations of hierarchical structures within ligands, receptors, or ligand-receptor unions. f Representations of hierarchical relations between ligand-receptor interactions.