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.

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.

Empirical data on contacts between individuals in social contexts play an important role in providing information for models describing human behavior and how epidemics spread in populations. Here, we analyze data on face-to-face contacts collected in an office building. The statistical properties of contacts are similar to other social situations, but important differences are observed in the contact network structure. In particular, the contact network is strongly shaped by the organization of the offices in departments, which has consequences in the design of accurate agent-based models of epidemic spread. We consider the contact network as a potential substrate for infectious disease spread and show that its sparsity tends to prevent outbreaks of rapidly spreading epidemics. Moreover, we define three typical behaviors according to the fraction f of links each individual shares outside its own department: residents, wanderers and linkers. Linkers ( f ∼ 50%) act as bridges in the network and have large betweenness centralities. Thus, a vaccination strategy targeting linkers efficiently prevents large outbreaks. As such a behavior may be spotted a priori in the offices' organization or from surveys, without the full knowledge of the time-resolved contact network, this result may help the design of efficient, low-cost vaccination or social-distancing strategies.

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.

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.

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.

Crescent-shaped barchan dunes are highly mobile dunes which are ubiquitous on Earth and other solar system bodies. Although they are unstable when considered separately, they form large assemblies in deserts and spatially organize in narrow corridors that extend in the wind direction. Collision of barchans has been proposed as a mechanism to redistribute sand between dunes and prevent the formation of very large dunes. Here we use an agent-based model with elementary rules of sand redistribution during collisions to access the full dynamics of very large barchan fields. We tune the dune field density by changing the sand load/lost ratio and follow the transition between dilute fields, where barchans barely interact, and dense filds, where dune collisions control and stabilize the dune field. In this dense regime, barchans have a small, well-selected size and form flocks: the dune field self-organizes in narrow corridors of dunes, as it is observed in real dense barchan deserts

Fundamental definitions and general results A. Temporal network B. Randomized reference model C. Combining microcanonical randomized reference models III. Features of temporal networks A. Notation for features of instant-event networks IV. Shuffling methods A. Link and timeline shufflings B. Sequence and snapshot shufflings V. Classifying randomized reference models A. Naming convention B. Applying instant-event shufflings to temporal networks with event durations C. The basic instant-event and event shufflings D. Link shufflings E. Timeline shufflings F. Sequence shufflings G. Snapshot shufflings H. Intersections of two shufflings I. Compositions of two shufflings J. Randomization based on metadata K. Other reference models VI. Analysis and hypothesis testing using randomized reference models A. Walkthrough example: analyzing face-to-face interactions using MRRMs B. Walkthrough example: analyzing temporal distances in a communication network using MRRMs VII. Applications of randomized reference models A. Contagion processes B. Random walks C. Evolutionary games D. Temporal motifs and networks with attributes E. Network controllability VIII. Conclusion A. Randomized reference models for directed temporal networks References * Multiple common names for a MRRM may exist; in these cases we report the others in the main text. † Feature only defined for temporal networks with event durations.