Social interactions are fundamental to human society, forming groups of varying sizes with communicative and collective advantages. While networks effectively represent pairwise interactions, most social interactions involve groups, necessitating higher-order network representations. Despite recent interest in higher-order networks, understanding the mechanisms governing group formation, evolution, and individual group navigation remains limited. This study uses empirical data from two distinct contexts—preschool children and university students—to analyze the temporal dynamics of group interactions at both individual and group levels. The aim is to characterize how individuals move between groups, and how groups assemble and disintegrate. The authors hypothesize that robust patterns exist across these diverse contexts, which can be captured by a novel dynamical model. Understanding these dynamics is crucial for characterizing emergent group behaviors and their impact on processes like disease transmission, information spread, and behavioral patterns within and across group gatherings. This research represents a significant step in understanding complex social systems by moving beyond the limitations of pairwise interaction analysis.

Existing research highlights the complexity of group interactions, including heterogeneous group sizes, dynamic changes, and hierarchical or nested structures. Potential driving mechanisms like simplicial closure and homophily have been proposed. However, most studies neglect the temporal evolution of these systems, overlooking patterns of memory, burstiness, and complex merging/splitting of groups. For instance, prior work suggests that larger groups tend to have shorter durations and shorter temporal correlations, exhibiting a preferred temporal direction in formation and fragmentation. The recurrence of groups, driven by contexts and locations, also shapes social circles. While these patterns stem from individual-level decisions, understanding the underlying mechanisms to characterize emergent group dynamics and their impact on various collective processes remains crucial.

The study leverages two datasets: the Copenhagen Network Study (CNS), tracking proximity events among university students using Bluetooth signals, and the DyLNet project, recording proximity interactions among preschool children using RFID sensors. Both datasets are temporally resolved, allowing for dynamic analysis. Groups are defined as maximal cliques (fully connected subgraphs) at each timestamp, constructing a temporal hypergraph. The CNS data is pre-processed to filter out weak interactions, smooth intermittent patterns, and perform triadic closure. The DyLNet data is pre-processed to focus on children's interactions and interactions lasting at least 10 seconds. Analysis includes examining group size distributions, transition matrices describing individual group changes, Jaccard similarity between consecutive groups, group duration distributions, and heatmaps showing group aggregation and disaggregation dynamics. A new dynamical model is introduced that explicitly accounts for group interactions, incorporating mechanisms of social and temporal memory. The model is parametrized and fitted to reproduce empirical patterns of group size distributions and node transition matrices using Kullback-Leibler (KL) divergence minimization. This model allows for agents to stay in their current group, leave to join a different one, or become isolated, with probabilities based on residence time and social memory.

The study reveals robust patterns across contexts. Group size distributions show similar shapes but varying ranges, with smaller groups preferred in unconstrained interaction contexts. Node transition matrices display consistent patterns: for smaller groups, the most probable next group size is the same size; distributions extend around the diagonal, with large differences in size being rare; and as group size increases, the probability of transitioning to smaller groups rises. Group duration distributions show a "long-gets-longer" effect, where the probability of group change decreases with time spent in the group. The distributions are broadly distributed for all group sizes and contexts with longer average and maximum durations observed for smaller group sizes, suggesting burstiness in node activity. Group aggregation and disaggregation exhibit symmetrical properties, with smaller groups changing gradually, while larger groups form from smaller ones and disintegrate into smaller subgroups. The proposed model accurately reproduces the empirical patterns of group size distributions, node transition matrices, group duration distributions, and aggregation/disaggregation dynamics, demonstrating its ability to capture the complexity of higher-order temporal interactions.

The findings demonstrate striking similarities in group dynamics across diverse contexts (preschool children and university students), suggesting common underlying mechanisms. The robustness of these patterns is further supported by supplementary analysis of data from scientific conferences. The proposed model, incorporating social and temporal memory, successfully reproduces these complex dynamics, highlighting the importance of considering both individual and group-level behaviors. The model offers a synthetic framework for future research on the impact of temporal higher-order interactions on various dynamical processes, such as social contagion, opinion formation, and cooperation, which have been studied with static hypergraphs but require more realistic temporal modelling. The model provides a more complete picture of social dynamics by moving beyond pairwise interactions.

This study provides novel insights into human group dynamics, revealing robust patterns across diverse contexts. The proposed model successfully captures the essential features of these dynamics and offers a valuable tool for studying the impact of group interactions on various collective phenomena. Future work could explore alternative definitions of groups, incorporate additional factors like homophily and opinion dynamics, and extend the model to non-human animal interactions, considering the influence of environmental and ecological factors.

The study's reliance on proximity data as a proxy for actual group interactions represents a limitation. The definition of groups as maximal cliques might not fully capture the nuances of real-world social interactions. Data sets differ in size and resolution, which could affect the generalizability of findings. Future research should address these limitations by exploring alternative group definitions and employing more comprehensive data collection methods.