[Paper Review] Higher-order modeling of face-to-face interactions

Luca Gallo, Chiara Zappalà+2 more|arXiv (Cornell University)|Jun 7, 2024

Data Visualization and Analytics4 citations

TL;DR

This paper introduces the Group Attractiveness Model (GAM), a higher-order agent-based framework that models face-to-face interactions through dynamic group formation, where group attractiveness—derived from member attractiveness—determines joining and leaving behaviors. The model successfully reproduces empirical group statistics, temporal persistence, and higher-order homophily patterns beyond pairwise interactions, offering a scalable mechanism for group-level social dynamics.

ABSTRACT

The most fundamental social interactions among humans occur face to face. Their features have been extensively studied in recent years, owing to the availability of high-resolution data on individuals' proximity. Mathematical models based on mobile agents have been crucial to understand the spatio-temporal organization of face-to-face interactions. However, these models focus on dyadic relationships only, failing to characterize interactions in larger groups of individuals. Here, we propose a model in which agents interact with each other by forming groups of different sizes. Each group has a degree of social attractiveness, based on which neighboring agents decide whether to join. Our framework reproduces different properties of groups in face-to-face interactions, including their distribution, the correlation in their number, and their persistence in time, which cannot be replicated by dyadic models. Furthermore, it captures homophilic patterns at the level of higher-order interactions, going beyond standard pairwise approaches. Our work sheds light on the higher-order mechanisms at the heart of human face-to-face interactions, paving the way for further investigation of how group dynamics at a microscopic scale affects social phenomena at a macroscopic scale.

Motivation & Objective

• To address the limitation of existing mobile agent models that focus only on dyadic interactions and fail to capture group-level dynamics in face-to-face encounters.
• To develop a modeling framework that reproduces key empirical features of group interactions, such as group size distribution, temporal correlation, and persistence.
• To investigate how higher-order homophily—homophily at the group level—emerges from individual attributes and group attractiveness, going beyond pairwise similarity.
• To provide a scalable, predictive model that enables the study of microscopic group dynamics and their macroscopic social consequences.

Proposed method

• Agents are placed in a 2D space with periodic boundaries and assigned individual attractiveness values uniformly drawn from [0,1].
• Group attractiveness is computed as the product of individual member attractivenesses, ensuring larger groups are less attractive on average.
• Agents decide to join or leave groups based on the group's attractiveness, with joining probability proportional to the group's attractiveness relative to others.
• The model tracks group formation and dissolution over time, using normalized fractions of group configurations to estimate homophily at both dyadic and triadic levels.
• Higher-order homophily is quantified using a 3D homophily matrix $ H^{(3)} $, where entries $ h_{etaetaeta} $ represent the probability of an agent with attribute $ eta $ joining a group of members with attributes $ eta $, $ eta $, $ eta $, etc.
• The model is validated by comparing simulated group statistics—such as size distribution, temporal persistence, and configuration fractions—to real-world face-to-face interaction data from schools and conferences.

Figure 1: Schematic illustration of the Group Attractiveness Model . At each time step $t$ , each active agent $i$ (blue) considers the groups lying within a radius $d$ from it, and interacts with all of them with a probability $p_{i}(t)$ that depends on the mean attractiveness of the neighboring gr

Experimental results

Research questions

• RQ1 Can a higher-order agent-based model reproduce the empirical statistics of group size, duration, and temporal correlation in real face-to-face interactions?
• RQ2 How does group attractiveness, derived from individual attractiveness, influence the formation and dissolution of social groups?
• RQ3 To what extent can the model capture higher-order homophily—homophily at the group level—beyond pairwise similarity?
• RQ4 How do group-level dynamics, such as schisming and reconfiguration, emerge from individual-level decisions based on attractiveness?
• RQ5 Can the model predict macroscopic social phenomena by simulating microscopic group interactions?

Key findings

• The Group Attractiveness Model successfully reproduces the empirical distribution of group sizes and their temporal persistence, which standard dyadic models fail to capture.
• The model captures the correlation in group numbers across time, showing that group dynamics are not independent but exhibit memory and clustering effects.
• The model reproduces higher-order homophily patterns: agents are more likely to join groups with similar attributes, and this preference is quantitatively measurable via the 3D homophily matrix $ H^{(3)} $.
• In the absence of homophily, the model reduces to a neutral case where $ h_{000} = h_{001} = h_{011} = 1/3 $, confirming consistency with baseline expectations.
• The model demonstrates that larger groups are less stable due to lower collective attractiveness, aligning with empirical observations of schisming in real social groups.
• The model’s predictive power is validated using real datasets from primary and high schools and scientific conferences, showing strong agreement with observed group-level statistics.

Figure 2: The GAM reproduces the empirical group statistics . Panels a to f report the distribution of groups of different sizes in a given social system (black circles), as well as the predictions of the Group Attractiveness Model (blue squares) and the Attractiveness Model [ 10 ] (red diamonds). M