Abstract

Higher-order networks are attracting large scientific interest in recent years. However, a key challenge is to infer higher-order interactions from data. Triadic interactions are a fundamental type of higher-order interactions that occur when one node regulates the interaction between two other nodes. We explore the fundamental dynamical properties of networks with triadic interactions between continuous variables. We formulate a general model of networks with triadic interactions. Moreover we propose an information theory framework and an algorithm, validated on the triadic model, that we call Triaction, that is able to mine triadic interactions from data and we apply this framework to gene expression data finding new candidates for triadic interactions relevant for Acute Myeloid Leukemia. In the future, the method could be applied to other type of data including times series relevant in climate research.