Fig. 1: Schematic representation of triadic interactions.

a A triadic interaction occurs when a node Z, called a regulator node, regulates (either positively or negatively) the interaction between two other nodes X and Y. The regulated edge can be conceptualized as a factor node (shown here as a cyan diamond). b A network with triadic interactions can be seen as a network of networks formed by a simple structural network and by a bipartite regulatory network between regulator nodes and regulated edges (factor nodes).