New research proposes using mathematical tool to decipher complex social dynamics

• Researchers at the Institute of Cross-disciplinary Physics and Complex Systems develop a model that characterises the dynamics of group interactions
• The study, published in ‘Nature Communications’, uses temporal hypergraphs to study how conversation groups form in different social contexts

Traditional network models describe interactions between peers. Because of this limitation, they fail to capture the dynamics of group interactions that characterise many real-world systems, such as real-time social conversations between three or more people. Other networks, such as those used in social, biological and ecological systems, often involve such interactions that are time-varying. Now, a new study published in Nature Communications proposes using a mathematical tool to unveil these complex and changing dynamics, with particular interest in social systems. The work, in which the Institute for Cross-disciplinary Physics and Complex Systems (IFISC-CSIC-UIB) participates, introduces a novel framework for analysing complex social systems through the lens of tools called temporal hypergraphs. This has made it possible to see how conversation groups form and dissolve in a social event.

A graph (or network) consists of elements (or nodes) connected by edges, with each edge linking exactly two vertices. On the other hand, a hypergraph allows, by means of so-called hyper-edges, to connect any number of vertices at the same time, from one to all the elements that are part of the hypergraph. This feature makes hypergraphs suitable tools for representing relationships involving several entities at the same time, such as research collaborations between several authors, group conversations or in databases, where traditional graphs might be insufficient to capture all the subtleties of the system.

The research, which also involved the Central European University of Vienna (Austria) and Queen Mary University of London (UK), introduces a set of measures designed to extract and analyse different parameters within hypergraphs. ‘Applying these measures to data on human interactions, such as the conversations that attendees of a scientific conference may have, we have demonstrated the existence of coherent and interdependent group structures that appear in these systems in a persistent way,’ explains Lucas Lacasa, researcher at IFISC-CSIC-UIB. These structures,’ adds Lacasa, ’reflect how conversation groups change over time, with people being added to them, fragmenting into smaller groups or forming new ones. For example, when a conversation involves too many people, it tends to fragment into two or more smaller groups.

Temporal hypergraphs

To better understand these dynamics, researchers introduced new theoretical models called temporal hypergraphs. Unlike previous models, these do not consider the connections between people to be fixed, but to change over time. These models introduce the idea of ‘complex memory’, i.e., interactions between people in the past affect how they will interact in the future. These new models have been useful for understanding how structures within groups remain stable or change, and how this affects the overall behaviour of the system over time.

To test the proposed framework, the research team analysed real data from 32 hours of face-to-face interactions between 403 participants at a scientific conference. They proposed a temporal hypergraph to represent group dynamics, in which each contact is modelled as a node connecting several individuals at the same time. The analyses revealed significant and prolonged temporal correlations, especially for groups of two to four people. In addition, the researchers found that interactions between groups of different sizes were also correlated. ‘These results suggest, for example, that the formation of five-person groups is more likely from a group of four that adds a new member than from a larger group that fragments into smaller groups of five. In other words, there is a preferential direction in the dynamics of nucleation and fragmentation of groups in this social system,’ says the IFISC-CSIC-UIB scientist.

The researchers' work represents an important step forward in network science, as it offers methodologies that can be applied to a wide range of disciplines. These include not only the social sciences, but also fields such as epidemiology, where understanding the dynamics of groups of populations can serve as a basis for improving disease control strategies, or even fields such as fluid dynamics, where the methodology can be applied to better understand the interaction between coherent groups of molecules, i.e. vortex-vortex interactions.

Luca Gallo, Lucas Lacasa, Vito Latora i Federico Battiston. Higher-order correlations reveal complex memory in temporal hypergraphs. Nature Communications. DOI: https://doi.org/10.1038/s41467-024-48578-6

• CSIC
• El diari de la UIB
• Dicyt
• The Smart City Journal
• La Palmesana