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

Promoting collective cooperation through temporal interactions

Collective cooperation maintains the function of many natural and social systems, making understanding the evolution of cooperation a central question of modern science. Although human interactions involve complex contact networks, current explorations are limited to static networks, where social ties are permanent and do not change over time. In reality, human activities often involve temporal interactions, where links are impermanent, and understanding the evolution of cooperation on such temporal networks is an open problem. Here, we systematically analyze how cooperation spreads on arbitrary temporal networks, and we distill our results down to a concise condition, which integrates evolutionary game dynamics with both static and temporal interactions. We find that the emergence of cooperation is facilitated by a simple rule of thumb: Hubs (individuals with many social ties) should be temporally deprioritized in interactions. For empirical applications, we further provide a quantitative metric capturing the priority of hubs, which is validated on empirical datasets based on its effectiveness in orchestrating the ordering of interactions to best promote cooperation. Our findings unveil the fundamental advantages conferred by temporal interactions for promoting collective cooperation, transcending the specific insights gleaned from studying static networks.

Drivers of cooperation in social dilemmas on higher-order networks

Understanding cooperation in social dilemmas requires models that capture the complexity of real-world interactions. While network frameworks have provided valuable insights to model the evolution of cooperation, they are unable to encode group interactions properly. Here, we introduce a general higher-order networks framework for multi-player games on structured populations. Our model considers multi-dimensional strategies, based on the observation that social behaviours are affected by the size of the group interaction. We investigate the dynamical and structural coupling between different orders of interactions, revealing the crucial role of nested multi-level interactions and showing how such features can enhance cooperation beyond the limit of traditional models with uni-dimensional strategies. Our work identifies the key drivers promoting cooperative behaviour commonly observed in real-world group social dilemmas.

Higher-order temporal network prediction and interpretation

A social interaction (so-called higher-order event/interaction) can be regarded as the activation of a hyperlink among the corresponding individuals. Social interactions can be, thus, represented as higher-order temporal networks that record the higher-order events occurring at each time step over time. The prediction of higher-order interactions is usually overlooked in traditional temporal network prediction methods, where a higher-order interaction is regarded as a set of pairwise interactions. The prediction of future higher-order interactions is crucial to forecast and mitigate the spread of information, epidemics and opinion on higher-order social contact networks. In this paper, we propose novel memory-based models for higher-order temporal network prediction. By using these models, we aim to predict the higher-order temporal network one time step ahead, based on the network observed in the past. Importantly, we also intend to understand what network properties and which types of previous interactions enable the prediction. The design and performance analysis of these models is supported by our analysis of the memory property of networks, e.g., similarity of the network and activity of a hyperlink over time, respectively. Our models assume that a target hyperlink's future activity (active or not) depends on the past activity of the target link and of all or selected types of hyperlinks that overlap with the target. We then compare the performance of our models with three baseline models, which are an activity driven model, a probabilistic group-change model and a pairwise temporal network prediction method. In eight real-world networks, we find that both our models consistently outperform the baselines. Moreover, the refined model, which only uses a subset of all types of overlapping hyperlinks, tends to perform the best. Our models also reveal how past interactions of the target hyperlink and different types of hyperlinks that overlap with the target contribute to the prediction of the target's future activity.

Patterns in Temporal Networks with Higher-Order Egocentric Structures

The analysis of complex and time-evolving interactions, such as those within social dynamics, represents a current challenge in the science of complex systems. Temporal networks stand as a suitable tool for schematizing such systems, encoding all the interactions appearing between pairs of individuals in discrete time. Over the years, network science has developed many measures to analyze and compare temporal networks. Some of them imply a decomposition of the network into small pieces of interactions; i.e., only involving a few nodes for a short time range. Along this line, a possible way to decompose a network is to assume an egocentric perspective; i.e., to consider for each node the time evolution of its neighborhood. This was proposed by Longa et al. by defining the "egocentric temporal neighborhood", which has proven to be a useful tool for characterizing temporal networks relative to social interactions. However, this definition neglects group interactions (quite common in social domains), as they are always decomposed into pairwise connections. A more general framework that also allows considering larger interactions is represented by higher-order networks. Here, we generalize the description of social interactions to hypergraphs. Consequently, we generalize their decomposition into "hyper egocentric temporal neighborhoods". This enables the analysis of social interactions, facilitating comparisons between different datasets or nodes within a dataset, while considering the intrinsic complexity presented by higher-order interactions. Even if we limit the order of interactions to the second order (triplets of nodes), our results reveal the importance of a higher-order representation.In fact, our analyses show that second-order structures are responsible for the majority of the variability at all scales: between datasets, amongst nodes, and over time.