The dynamics of social systems with higher-order interactions

Networks are made of nodes and links. Hence, they model well dynamical processes, such as the spreading of a disease in a population, where transmission occurs through pairwise contacts. Conversely, networks are not best suited to describe the spreading of innovation, the formation of opinions or the emergence of cooperation in social systems, all processes in which more complex mechanisms of interactions, involving groups of three or more units, are at work. In this talk, I will discuss how to use higher-order networks to better model the presence and role of groups in different types of social dynamics. With the analysis of a series of study cases, I will show that higher-order interactions produce novel collective phenomena. They lead to explosive transitions to the adoption of novelties in models of social contagion, stabilize otherwise unstable synchronized states in systems of many-body dynamical units, and even  provide novel explanation for the survival of cooperation in social dilemmas.

The effect of transitivity on complex contagion

Social decision making, be it adoption of technology, sharing of opinions or spread of social movements, is often modelled as complex contagion, in which support from multiple neighbours is necessary before an agent adopts a new state. Meanwhile, social networks are marked by a high degree of clustering or transitivity, which creates feedback loops between neighbours. This lack of independence between the first neighbours of an agent profoundly affects the dynamics of complex contagion. The simplest case of complex contagion is when an agent adopts an opinion when two or more of their neighbours have adopted it. To demonstrate the effect of transitivity on complex contagion, I will describe this minimal complex contagion on an STC model network. In this network, triads are randomly closed in a backbone network, forming triangles, thus allowing for the creation of highly random networks with controllable transitivity. I will show how the presence of transitivity enhances the spread of opinions in complex contagion. A much smaller number of agents need to be 'seeded' with the opinion initially to achieve the same final level of adoption. If the transitivity is sufficiently large, widespread adoption is possible with an arbitrarily small initial seeding, a phenomenon which cannot be observed in locally treelike networks. The percolation of edge-adjacent triangles creates the conditions for this long range spread across the social network.

Strongly clustered random graphs via triadic closure: exact solutions and the role of short loops

In this talk, I present a static triadic closure (STC) model for clustered networks, where triads are independently closed on a fixed backbone network. Assuming a locally treelike backbone, exact expressions for the expected number of various small, loopy motifs can be derived in terms of the backbone degree distribution's moments. Furthermore, approximate motif density relationships are validated against real-world networks, showing a good agreement. Despite their complex structure with overlapping loops, we provide the exact solution for site percolation on large STC random networks by mapping to extended-range percolation on the backbone. This solution allows us to compute critical exponents and challenges the validity of the heterogeneous mean-field universality class for percolation in complex networks.

Higher-order modeling of face-to-face interactions

The most fundamental social interactions among humans occur face-to-face. Mathematical models based on mobile agents have been crucial to understanding their spatio-temporal organization. However, most models focus on dyadic relationships only, failing to characterize interactions in larger groups of individuals. In this talk, I describe a model where agents interact with each other by forming groups of different sizes. This model reproduces different properties of groups in face-to-face interactions, including their distribution, the correlation in their number, and their persistence in time. Furthermore, it captures homophilic patterns beyond pairwise interactions.

Exploring temporal triadic closure patterns in online social networks

Triadic closure—the tendency for “friends of friends” to connect—is a universal force in social networks, but its temporal dynamics remain underexplored. We present a framework to detect, characterize, and time the rules behind triadic closure across diverse online platforms, from email to Web3. Our results uncover both shared mechanisms and striking platform-specific signatures, offering new insights into how online social structures evolve.