Battiston Leads Review on the Structure and Dynamics of Higher-Order Networks

The complex patterns of interactions that we see in many systems, from social networks to the human brain, are key to understanding their behavior says Federico Battiston, Assistant Professor in CEU’s Department of Network and Data Science.

Battiston’s latest research looks at how a virus spreads in a population: “Knowing the properties of the single individual’s age, illnesses, gender and so on is not enough to understand and possibly predict the evolution of a pandemic. Much more crucial information is provided by an accurate description of the connections in a population.”

With strong roots in social network analysis and graph theory, network science has become a well-defined discipline over the past 20 years, with direct applications from ecology to neuroscience. Yet the study of complex systems has focused exclusively on interactions between dyads - simple pairs of entities. More recently, however, this approach has shown its limitations. “Human interactions are not limited to pairs, but often occur in large groups,” Battiston explains. “Think of online and offline interactions, where three or more people often connect together at the same time. Considering these higher-order interactions is very important for understanding the collective behavior of a population. For instance, we might not adapt a social norm like wearing a mask by simply imitating a neighbor, but we might feel socially pressured to do it if we are part of a larger group and there is a consolidated majority that pushes for this.”

Prompted by this and similar shortcomings, Battiston led a team (1) that has published a new paper in Physics Reports, “Networks Beyond Pairwise Interactions: Structure and Dynamics.” The article highlights the importance of turning away from reductionism and focusing instead on understanding the global architecture of relationships between units — individuals, neurons, ecological species and so on — rather than their specific features. “Embracing complexity is necessary to explain what we witness in the real world,” Battiston maintains . “If the interactions between units are so important to understanding emerging patterns and collective behavior, we need to be accurate while describing them. Pairwise interactions are surely not enough to capture how nature works.”

“Investigating higher-order systems seems particularly promising in many social and biological systems, where we know – or we strongly suspect – that interactions between elements are mediated or modulated by other elements,” adds Giovanni Petri, researcher at the ISI Foundation and co-author of the paper. “An outstanding question, however, is how can we generally measure the presence and strength of these interactions?”

The first part of the review looks at understanding how networks with higher-order interactions can be modeled, and how the degree of relevance for these group interactions can be measured. The second part investigates how the existence of higher-order interactions can change the emerging patterns and dynamics of many real-world systems. “Higher-order interactions are ubiquitous and not limited to processes of social contagion,” Battiston emphasizes. “They determine how many entities — for instance neurons in the brain — may synchronize. Additionally, they also affect ecosystems, where multiple species interact with each other to create complex, often delicate equilibria.”

With 800 references and at almost 100 pages in length, the report by Battiston and his co-authors is the largest and most comprehensive paper to date in the field of complexity science, and will be a useful source for many network scientists in the years to come.


1) Federico Battiston (CEU); Giulia Cencetti (Fondazione Bruno Kessler); Iacopo Iacopini (Queen Mary University of London / University College London); Vito Latora (Queen Mary University London / Universita di Catania / The Alan Turing Institute / Complexity Science Hub Vienna); Maxime Lucas (Aix-Marseille University); Alice Patania (Indiana University Bloomington); Jean-Gabriel Young (University of Michigan); Giovanni Petri (ISI Global Science Foundation)