Modeling framework unifying contact and social networks.

Temporal networks of face-to-face interactions between individuals are useful proxies of the dynamics of social systems on fast timescales. Several empirical statistical properties of these networks have been shown to be robust across a large variety of contexts. To better grasp the role of various mechanisms of social interactions in the emergence of these properties, models in which schematic implementations of such mechanisms can be carried out have proven useful. Here, we put forward a framework to model temporal networks of human interactions based on the idea of a coevolution and feedback between (i) an observed network of instantaneous interactions and (ii) an underlying unobserved social bond network: Social bonds partially drive interaction opportunities and in turn are reinforced by interactions and weakened or even removed by the lack of interactions. Through this coevolution, we also integrate in the model well-known mechanisms such as triadic closure, but also the impact of shared social context and nonintentional (casual) interactions, with several tunable parameters. We then propose a method to compare the statistical properties of each version of the model with empirical face-to-face interaction data sets to determine which sets of mechanisms lead to realistic social temporal networks within this modeling framework.

The switching mechanisms of social network densification.

Densification and sparsification of social networks are attributed to two fundamental mechanisms: a change in the population in the system, and/or a change in the chances that people in the system are connected. In theory, each of these mechanisms generates a distinctive type of densification scaling, but in reality both types are generally mixed. Here, we develop a Bayesian statistical method to identify the extent to which each of these mechanisms is at play at a given point in time, taking the mixed densification scaling as input. We apply the method to networks of face-to-face interactions of individuals and reveal that the main mechanism that causes densification and sparsification occasionally switches, the frequency of which depending on the social context. The proposed method uncovers an inherent regime-switching property of network dynamics, which will provide a new insight into the mechanics behind evolving social interactions.

Two types of densification scaling in the evolution of temporal networks.

Many real-world social networks constantly change their global properties over time, such as the number of edges, size, and density. While temporal and local properties of social networks have been extensively studied, the origin of their dynamical nature is not yet well understood. Networks may grow or shrink if (a) the total population of nodes changes and/or (b) the chance of two nodes being connected varies over time. Here, we develop a method that allows us to classify the source of time-varying nature of temporal networks. In doing so, we first show empirical evidence that real-world dynamical systems could be categorized into two classes, the difference of which is characterized by the way the number of edges grows with the number of active nodes, i.e., densification scaling. We develop a dynamic hidden-variable model to formally characterize the two dynamical classes. The model is fitted to the empirical data to identify whether the origin of scaling comes from a changing population in the system or shifts in the connecting probabilities.

Correction: Temporal Gillespie algorithm: Fast simulation of contagion processes on time-varying networks.

[This corrects the article DOI: 10.1371/journal.pcbi.1004579.].

Homophily influences ranking of minorities in social networks.

Homophily can put minority groups at a disadvantage by restricting their ability to establish links with a majority group or to access novel information. Here, we show how this phenomenon can influence the ranking of minorities in examples of real-world networks with various levels of heterophily and homophily ranging from sexual contacts, dating contacts, scientific collaborations, and scientific citations. We devise a social network model with tunable homophily and group sizes, and demonstrate how the degree ranking of nodes from the minority group in a network is a function of (i) relative group sizes and (ii) the presence or absence of homophilic behaviour. We provide analytical insights on how the ranking of the minority can be improved to ensure the representativeness of the group and correct for potential biases. Our work presents a foundation for assessing the impact of homophilic and heterophilic behaviour on minorities in social networks.

Out-of-equilibrium stationary states, percolation, and subcritical instabilities in a fully nonconservative system.

The exploration of the phase diagram of a minimal model for barchan fields leads to the description of three distinct phases for the system: stationary, percolable, and unstable. In the stationary phase the system always reaches an out-of-equilibrium, fluctuating, stationary state, independent of its initial conditions. This state has a large and continuous range of dynamics, from dilute-where dunes do not interact-to dense, where the system exhibits both spatial structuring and collective behavior leading to the selection of a particular size for the dunes. In the percolable phase, the system presents a percolation threshold when the initial density increases. This percolation is unusual, as it happens on a continuous space for moving, interacting, finite lifetime dunes. For extreme parameters, the system exhibits a subcritical instability, where some of the dunes in the field grow without bound. We discuss the nature of the asymptotic states and their relations to well-known models of statistical physics.

Recalibrating disease parameters for increasing realism in modeling epidemics in closed settings.

BACKGROUND: The homogeneous mixing assumption is widely adopted in epidemic modelling for its parsimony and represents the building block of more complex approaches, including very detailed agent-based models. The latter assume homogeneous mixing within schools, workplaces and households, mostly for the lack of detailed information on human contact behaviour within these settings. The recent data availability on high-resolution face-to-face interactions makes it now possible to assess the goodness of this simplified scheme in reproducing relevant aspects of the infection dynamics. METHODS: We consider empirical contact networks gathered in different contexts, as well as synthetic data obtained through realistic models of contacts in structured populations. We perform stochastic spreading simulations on these contact networks and in populations of the same size under a homogeneous mixing hypothesis. We adjust the epidemiological parameters of the latter in order to fit the prevalence curve of the contact epidemic model. We quantify the agreement by comparing epidemic peak times, peak values, and epidemic sizes. RESULTS: Good approximations of the peak times and peak values are obtained with the homogeneous mixing approach, with a median relative difference smaller than 20 % in all cases investigated. Accuracy in reproducing the peak time depends on the setting under study, while for the peak value it is independent of the setting. Recalibration is found to be linear in the epidemic parameters used in the contact data simulations, showing changes across empirical settings but robustness across groups and population sizes. CONCLUSIONS: An adequate rescaling of the epidemiological parameters can yield a good agreement between the epidemic curves obtained with a real contact network and a homogeneous mixing approach in a population of the same size. The use of such recalibrated homogeneous mixing approximations would enhance the accuracy and realism of agent-based simulations and limit the intrinsic biases of the homogeneous mixing.

Compensating for population sampling in simulations of epidemic spread on temporal contact networks.

Data describing human interactions often suffer from incomplete sampling of the underlying population. As a consequence, the study of contagion processes using data-driven models can lead to a severe underestimation of the epidemic risk. Here we present a systematic method to alleviate this issue and obtain a better estimation of the risk in the context of epidemic models informed by high-resolution time-resolved contact data. We consider several such data sets collected in various contexts and perform controlled resampling experiments. We show how the statistical information contained in the resampled data can be used to build a series of surrogate versions of the unknown contacts. We simulate epidemic processes on the resulting reconstructed data sets and show that it is possible to obtain good estimates of the outcome of simulations performed using the complete data set. We discuss limitations and potential improvements of our method.

Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks.

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.

How memory generates heterogeneous dynamics in temporal networks.

Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks, little work has been devoted to the understanding of how such heterogeneities can emerge from microscopic mechanisms at the level of nodes and links. Here we show that long-term memory effects are present in the creation and disappearance of links in empirical networks. We thus consider a simple generative modeling framework for temporal networks able to incorporate these memory mechanisms. This allows us to study separately the role of each of these mechanisms in the emergence of heterogeneous network dynamics. In particular, we show analytically and numerically how heterogeneous distributions of contact durations, of intercontact durations, and of numbers of contacts per link emerge. We also study the individual effect of heterogeneities on dynamical processes, such as the paradigmatic susceptible-infected epidemic spreading model. Our results confirm in particular the crucial role of the distributions of intercontact durations and of the numbers of contacts per link.