The temporal dynamics of group interactions in higher-order social networks

TL;DR

Empirical data on social interactions among children and university students is leveraged to study their temporal dynamics at both individual and group levels, characterising how individuals navigate groups and how groups form and disaggregate and proposes a dynamical model that closely reproduces empirical observations.

Abstract

Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur among groups of individuals, requiring higher-order network representations. Despite the recent interest in higher-order networks, little is known about the mechanisms that govern the formation and evolution of groups, and how people move between groups. Here, we leverage empirical data on social interactions among children and university students to study their temporal dynamics at both individual and group levels, characterising how individuals navigate groups and how groups form and disaggregate. We find robust patterns across contexts and propose a dynamical model that closely reproduces empirical observations. These results represent a further step in understanding social systems, and open up research directions to study the impact of group dynamics on dynamical processes that evolve on top of them.

Figures (30)

• Figure 1: ( A-B) Group size distributions for University ( A) and Preschool ( B) interactions that take place in-class, out-of-class, or during the weekend (see legend). ( C-G) Node transition matrices for University ( C-E) and Preschool ( F-G), for interactions that take place during in-class ( E,F), out-of-class ( C,G), or weekend ( D) time. The elements of each matrix represent the conditional probability that a node that is member of a group of size $k$ at time $t$ is next member of a different group of size $k^{\prime}$ at time $t+1$ ---given that it undergoes a group change between $t$ and $t+1$. Probability values are given by the height of each element (normalized by row). Note that the scales on the y-axes ---one for each matrix row--- vary for visualization purposes.
• Figure 2: Distributions of group durations $\tau$ for the CNS ( A-C) and the DyLNet ( D-E) data sets in different contexts: in-class ( A,D), out-of-class ( B,E) and weekend ( C). In each panel, different symbols correspond to different group sizes. The distributions for group size $1$ have been fitted using the method in Ref. alstott2014powerlaw, and can be characterized by the depicted exponent values.
• Figure 3: Group dynamics of aggregation and disaggregation for University ( A-C) and Preschool ( D-E) interactions that take place during in-class ( A,D), out-of-class ( B,E), or weekend ( C) time. Each side of the pyramidal heatmaps shows the probability distribution associated to the size for the largest sub-group joining and the largest subgroup leaving a group of size $k$. The central column reports the considered group size $k$, while the probability distributions on its left-hand side and right-hand side respectively corresponds to group aggregation and disaggregation. Dashed lines refer to the distribution average.
• Figure 4: Fitting the empirical group-change probability and measuring the signal of social memory for the out-of-class interactions from the CNS ( A-C) and the DyLNet ( D-F) data sets. ( A,D) Probability for a node belonging to a group of any size to leave it for a different one after exactly $\tau$ timestamps. Points are binned empirical results, dashed lines represent a power-law fit of the form $b\tau^{\beta}$ ---values reported in each panel. Fitted exponents $\beta$ are then used to estimate the group-size-dependent constants $b_k$, as given in Eq. \ref{['eq:group_change']}, with another power-law fit. In ( B,E) the resulting values for $b_k$ are plotted (points and 95% CI error bars) together with a logistic fit (dashed lines). ( C,F) Distribution of fraction of nodes ---composing a newly chosen group--- that were previously known to the focal node. The resulting distributions of values, averaged over the different time steps, are plotted in comparison to two null scenarios where the group to join is chosen at random, or at random given the target size.
• Figure 5: Simulated distribution of group size ( A), node transition matrix ( B), group duration for different group sizes $k$ ( C), and pyramidal heatmap associated to the aggregation and disaggregation dynamics ( D) generated by the proposed temporal hypergraph model.