The structure of higher-order interaction networks

From nature to society, we are surrounded by systems whose organization can appear very complicated. Billions of individuals coordinate and cooperate in human societies. Billions of cell phones with computers and satellites are integrated in communications infrastructures. Our brain functions because of the coherent activity of billions of neurons. Humans, cell phones and neurons are very different objects. Yet, all such systems are collectively called complex systems to describe the fact that it is difficult to derive their collective behavior and functionality from the knowledge of the systems components only. Over the past decades, a variety of complex systems have been successfully described as networks, where system units are represented as nodes, and interactions are encoded through links. This approach has brought new insights into a variety of different realms. For instance, we have discovered that efficient communication structures are suited to reach rapid and diffused consensus, but are also prone to the unwanted spreading of misinformation or of dangerous infectious diseases. Despite their success, it is now becoming clear that graphs can only provide a limited description of reality. Indeed, networks are inherently constrained to represent systems with pairwise interactions only, since interactions are described by links, which can only connect two nodes at a time. Yet, in many biological, physical and social systems, system components may interact in larger groups. For instance, some medicine cocktails are only effective when three or more drugs are combined together. Similarly, human discoveries increasingly rely on the coordinated work of teams with multiple members. Many achievements are only possible because of the coordinated synergistic efforts of multiple system components, exceeding what could be obtained by two interacting units only. This observation calls for a new fundamental switch in the way we think, understand and analyse real-world relational systems with group interactions. This project aims to overcome the prominent, yet intrinsically limited network descriptions of interacting systems, with the goal to embrace a new and more general approach to complex systems. We will propose new measures to capture the higher-order, non-dyadic organization of real-world relational systems, and new mathematical and computational models able to explain the observed patterns. Beyond traditional graphs, the new higher-order paradigm will allow us to encode complexity in a much more comprehensive manner, taking a step forward in our understanding of natural, social and man-made emerging phenomena.

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