Explore the vast range of titles available.

Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems. Social contagion cannot only be understood in terms of pairwise interactions among individuals. Here, the authors include higher-order social interactions, the effects of groups, in their model of social contagion, enabling insight into why critical masses are required to initiate social changes.

Face-to-face contacts between individuals contribute to shape social networks and play an important role in determining how infectious diseases can spread within a population. It is thus important to obtain accurate and reliable descriptions of human contact patterns occurring in various day-to-day life contexts. Recent technological advances and the development of wearable sensors able to sense proximity patterns have made it possible to gather data giving access to time-varying contact networks of individuals in specific environments. Here we present and analyze two such data sets describing with high temporal resolution the contact patterns of students in a high school. We define contact matrices describing the contact patterns between students of different classes and show the importance of the class structure. We take advantage of the fact that the two data sets were collected in the same setting during several days in two successive years to perform a longitudinal analysis on two very different timescales. We show the high stability of the contact patterns across days and across years: the statistical distributions of numbers and durations of contacts are the same in different periods, and we observe a very high similarity of the contact matrices measured in different days or different years. The rate of change of the contacts of each individual from one day to the next is also similar in different years. We discuss the interest of the present analysis and data sets for various fields, including in social sciences in order to better understand and model human behavior and interactions in different contexts, and in epidemiology in order to inform models describing the spread of infectious diseases and design targeted containment strategies.

Given their importance in shaping social networks and determining how information or transmissible diseases propagate in a population, interactions between individuals are the subject of many data collection efforts. To this aim, different methods are commonly used, ranging from diaries and surveys to decentralised infrastructures based on wearable sensors. These methods have each advantages and limitations but are rarely compared in a given setting. Moreover, as surveys targeting friendship relations might suffer less from memory biases than contact diaries, it is interesting to explore how actual contact patterns occurring in day-to-day life compare with friendship relations and with online social links. Here we make progresses in these directions by leveraging data collected in a French high school and concerning (i) face-to-face contacts measured by two concurrent methods, namely wearable sensors and contact diaries, (ii) self-reported friendship surveys, and (iii) online social links. We compare the resulting data sets and find that most short contacts are not reported in diaries while long contacts have a large reporting probability, and that the durations of contacts tend to be overestimated in the diaries. Moreover, measured contacts corresponding to reported friendship can have durations of any length but all long contacts do correspond to a reported friendship. On the contrary, online links that are not also reported in the friendship survey correspond to short face-to-face contacts, highlighting the difference of nature between reported friendships and online links. Diaries and surveys suffer moreover from a low sampling rate, as many students did not fill them, showing that the sensor-based platform had a higher acceptability. We also show that, despite the biases of diaries and surveys, the overall structure of the contact network, as quantified by the mixing patterns between classes, is correctly captured by both networks of self-reported contacts and of friendships, and we investigate the correlations between the number of neighbors of individuals in the three networks. Overall, diaries and surveys tend to yield a correct picture of the global structural organization of the contact network, albeit with much less links, and give access to a sort of backbone of the contact network corresponding to the strongest links, i.e., the contacts of longest cumulative durations.

Technological advances have led to a strong increase in the number of data collection efforts aimed at measuring co-presence of individuals at different spatial resolutions. It is however unclear how much co-presence data can inform us on actual face-to-face contacts, of particular interest to study the structure of a population in social groups or for use in data-driven models of information or epidemic spreading processes. Here, we address this issue by leveraging data sets containing high resolution face-to-face contacts as well as a coarser spatial localisation of individuals, both temporally resolved, in various contexts. The co-presence and the face-to-face contact temporal networks share a number of structural and statistical features, but the former is (by definition) much denser than the latter. We thus consider several down-sampling methods that generate surrogate contact networks from the co-presence signal and compare them with the real face-to-face data. We show that these surrogate networks reproduce some features of the real data but are only partially able to identify the most central nodes of the face-to-face network. We then address the issue of using such down-sampled co-presence data in data-driven simulations of epidemic processes, and in identifying efficient containment strategies. We show that the performance of the various sampling methods strongly varies depending on context. We discuss the consequences of our results with respect to data collection strategies and methodologies.

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. The structure and dynamics of many social systems where human interactions involve communities can be described by higher-order networks. The authors propose a hypergraph-based model that describes how individuals form groups and navigate between groups of different sizes.

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hypercoreness. We assess the role of hyper-cores and nodes with large hypercoreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hypercoreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs. Networks with higher-order interactions provide better description of social and biological systems, however tools to analyze their function still need to be developed. The authors introduce here a decomposition of network in hyper-cores, that gives better understanding of spreading processes and can be applied to fingerprint real-world datasets.

How does the spread of behavior affect consensus-based collective decision-making among animals, humans or swarming robots? In prior research, such propagation of behavior on social networks has been found to exhibit a transition from simple contagion—i.e, based on pairwise interactions—to a complex one—i.e., involving social influence and reinforcement. However, this rich phenomenology appears so far limited to threshold-based decision-making processes with binary options. Here, we show theoretically, and experimentally with a multi-robot system, that such a transition from simple to complex contagion can also be observed in an archetypal model of distributed decision-making devoid of any thresholds or nonlinearities. Specifically, we uncover two key results: the nature of the contagion—simple or complex—is tightly related to the intrinsic pace of the behavior that is spreading, and the network topology strongly influences the effectiveness of the behavioral transmission in ways that are reminiscent of threshold-based models. These results offer new directions for the empirical exploration of behavioral contagions in groups, and have significant ramifications for the design of cooperative and networked robot systems. In consensus-based collective dynamics, the occurrence of simple and complex contagions shapes system behavior. The authors analyze a transition from simple to complex contagions in collective decision-making processes based on consensus, and demonstrate it with a swarm robotic system.

In many data sets, information on the structure and temporality of a system coexists with noise and non-essential elements. In networked systems for instance, some edges might be non-essential or exist only by chance. Filtering them out and extracting a set of relevant connections is a non-trivial task. Moreover, mehods put forward until now do not deal with time-resolved network data, which have become increasingly available. Here we develop a method for filtering temporal network data, by defining an adequate temporal null model that allows us to identify pairs of nodes having more interactions than expected given their activities: the significant ties. Moreover, our method can assign a significance to complex structures such as triads of simultaneous interactions, an impossible task for methods based on static representations. Our results hint at ways to represent temporal networks for use in data-driven models. Complex networks can be useful to describe social interactions but for large datasets one needs to identify significant links to extract information. While most existing methods work for static networks, here the authors propose a method to extract the backbone of significant links in temporal networks.

Background School environments are thought to play an important role in the community spread of infectious diseases such as influenza because of the high mixing rates of school children. The closure of schools has therefore been proposed as an efficient mitigation strategy. Such measures come however with high associated social and economic costs, making alternative, less disruptive interventions highly desirable. The recent availability of high-resolution contact network data from school environments provides an opportunity to design models of micro-interventions and compare the outcomes of alternative mitigation measures. Methods and results We model mitigation measures that involve the targeted closure of school classes or grades based on readily available information such as the number of symptomatic infectious children in a class. We focus on the specific case of a primary school for which we have high-resolution data on the close-range interactions of children and teachers. We simulate the spread of an influenza-like illness in this population by using an SEIR model with asymptomatics, and compare the outcomes of different mitigation strategies. We find that targeted class closure affords strong mitigation effects: closing a class for a fixed period of time – equal to the sum of the average infectious and latent durations – whenever two infectious individuals are detected in that class decreases the attack rate by almost 70% and significantly decreases the probability of a severe outbreak. The closure of all classes of the same grade mitigates the spread almost as much as closing the whole school. Conclusions Our model of targeted class closure strategies based on readily available information on symptomatic subjects and on limited information on mixing patterns, such as the grade structure of the school, shows that these strategies might be almost as effective as whole-school closure, at a much lower cost. This may inform public health policies for the management and mitigation of influenza-like outbreaks in the community.

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions.