Networks beyond pairwise interactions: a first comprehensive overview on structure and dynamics of higher-order complex systems

Sometimes it takes a lot of time. After eight years working at the interface of topological data analysis and network theory, ISI Foundation Senior Research Scientist Giovanni Petri has led an international team of researchers, including former ISI Junior Researchers Alice Patania and Iacopo Iacopini, to compile, elaborate and present one of the first complete overviews of the emerging field of networks beyond pairwise interactions. Already out in arXiv, the paper has been accepted and will be published in Physics Reports.

«The complexity of many biological, social and technological systems stems from the richness of the interactions among their units», say the scientists. «Over the past decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, in face-to-face human communication,  chemical reactions and ecological systems, interactions can occur in groups of three or more nodes. Until recently, little attention has been devoted to the higher-order architecture of real complex systems».

In a deep 109-pages analysis, scientists first discuss the methods to represent higher-order interactions, then they review the measures designed to characterize the structure of these systems and the models proposed in the literature to generate synthetic structures. They introduce and discuss the rapidly growing research on higher-order dynamical systems and on dynamical topology. Finally they focus on novel emergent phenomena characterizing landmark dynamical processes extended  beyond pairwise interactions (diffusion, spreading, synchronization,  games), and conclude with a summary of empirical applications, providing an outlook on current modeling and conceptual frontiers.

“Networks  beyond pairwise interactions: structure and dynamics”, Federico  Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas,  Alice Patania, Jean-Gabriel Young, Giovanni Petri. Link