High-resolution measurements of face-to-face contact patterns in a primary school

Individual-centralized seeding strategy for influence maximization in information-limited networks

Peer effects can directly or indirectly rely on interaction networks to drive people to follow ideas or behaviours triggered by a few individuals, and such effects can be largely improved by targeting the so-called influential individuals. In this article, we study the current most promising seeding strategy used in field experiments, the one-hop strategy, where the underlying interaction networks are generally too impractical or prohibitively expensive to be obtained, and propose an individual-centralized seeding approach to target influential seeds in information-limited networks. The presented strategy works by reasonable follow-up questions to respondents, such as Who do you think has more connections/friends?, and constructs the seeding set by those nodes with the most nominations. In this manner, the proposed method could acquire more information about the studied interaction network from the inference of respondents without surveying additional individuals. We evaluate our strategy on networks from various experimental datasets. Results show that the obtained seeds are much more influential compared to the one-hop strategy and other methods. We also show how the proposed approach could be implemented in field studies and potentially provide better interventions in real scenarios.

Community detection in hypergraphs via mutual information maximization

The hypergraph community detection problem seeks to identify groups of related vertices in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community labels and community-edge intersections. This algorithm can also be viewed as maximum-likelihood inference in a degree-corrected microcanonical stochastic blockmodel. We perform the compression/inference step via simulated annealing. Unlike several recent algorithms based on canonical models, our microcanonical algorithm does not require inference of statistical parameters such as vertex degrees or pairwise group connection rates. Through synthetic experiments, we find that our algorithm succeeds down to recently-conjectured thresholds for sparse random hypergraphs. We also find competitive performance in cluster recovery tasks on several hypergraph data sets.

Analysis of SARS-CoV-2 transmission in a university classroom based on real human close contact behaviors

Due to high-population density, frequent close contact, possible poor ventilation, university classrooms are vulnerable for transmission of respiratory infectious diseases. Close contact and long-range airborne are possibly main routes for SARS-CoV-2 transmission. In this study, taking a university classroom in Beijing for example, close contact behaviors of students were collected through a depth-detection device, which could detect depth to each pixel of the image, based on semi-supervised learning. Finally, >23 h of video data were obtained. Using Computational Fluid Dynamics, the relationship between viral exposure and close contact behaviors (e.g. interpersonal distance, relative facial orientations, and relative positions) was established. A multi-route transmission model (short-range airborne, mucous deposition, and long-range airborne) of infectious diseases considering real close contact behaviors was developed. In the case of Omicron, the risk of infection in university classrooms and the efficacy of different interventions were assessed based on dose-response model. The average interpersonal distance in university classrooms is 0.9 m (95 % CI, 0.5 m-1.4 m), with the highest proportion of face-to-back contact at 87.0 %. The risk of infection of susceptible students per 45-min lesson was 1 %. The relative contributions of short-range airborne and long-range airborne transmission were 40.5 % and 59.5 %, respectively, and the mucous deposition was basically negligible. When all students are wearing N95 respirators, the infection risk could be reduced by 96 %, the relative contribution of long-range airborne transmission increases to 95.6 %. When the fresh air per capita in the classroom is 24 m3/h/person, the virus exposure could be decreased by 81.1 % compared to the real situation with 1.02 m3/h/person. In a classroom with an occupancy rate of 50 %, after optimized arrangement of student distribution, the infection risk could be decreased by 62 %.

Higher-order homophily on simplicial complexes

Higher-order network models are becoming increasingly relevant for their ability to explicitly capture interactions between three or more entities in a complex system at once. In this paper, we study homophily, the tendency for alike individuals to form connections, as it pertains to higher-order interactions. We find that straightforward extensions of classical homophily measures to interactions of size 3 and larger are often inflated by homophily present in pairwise interactions. This inflation can even hide the presence of anti-homophily in higher-order interactions. Hence, we develop a structural measure of homophily, simplicial homophily, which decouples homophily in pairwise interactions from that of higher-order interactions. The definition applies when the network can be modeled as a simplicial complex, a mathematical abstraction which makes a closure assumption that for any higher-order relationship in the network, all corresponding subsets of that relationship occur in the data. Whereas previous work has used this closure assumption to develop a rich theory in algebraic topology, here we use the assumption to make empirical comparisons between interactions of different sizes. The simplicial homophily measure is validated theoretically using an extension of a stochastic block model for simplicial complexes and empirically in large-scale experiments across 16 datasets. We further find that simplicial homophily can be used to identify when node features are valuable for higher-order link prediction. Ultimately, this highlights a subtlety in studying node features in higher-order networks, as measures defined on groups of size k can inherit features described by interactions of size [Formula: see text].

Estimating household contact matrices structure from easily collectable metadata

Contact matrices are a commonly adopted data representation, used to develop compartmental models for epidemic spreading, accounting for the contact heterogeneities across age groups. Their estimation, however, is generally time and effort consuming and model-driven strategies to quantify the contacts are often needed. In this article we focus on household contact matrices, describing the contacts among the members of a family and develop a parametric model to describe them. This model combines demographic and easily quantifiable survey-based data and is tested on high resolution proximity data collected in two sites in South Africa. Given its simplicity and interpretability, we expect our method to be easily applied to other contexts as well and we identify relevant questions that need to be addressed during the data collection procedure.

An automated, data-driven approach to children's social dynamics in space and time

Most children first enter social groups of peers in preschool. In this context, children use movement as a social tool, resulting in distinctive proximity patterns in space and synchrony with others over time. However, the social implications of children's movements with peers in space and time are difficult to determine due to the difficulty of acquiring reliable data during natural interactions. In this article, we review research demonstrating that proximity and synchrony are important indicators of affiliation among preschoolers and highlight challenges in this line of research. We then argue for the advantages of using wearable sensor technology and machine learning analytics to quantify social movement. This technological and analytical advancement provides an unprecedented view of complex social interactions among preschoolers in natural settings, and can help integrate young children's movements with others in space and time into a coherent interaction framework.

Transmission matrices used in epidemiologic modelling

Mixing matrices are included in infectious disease models to reflect transmission opportunities between population strata. These matrices were originally constructed on the basis of theoretical considerations and most of the early work in this area originates from research on sexually transferred diseases in the 80s, in response to AIDS. Later work in the 90s populated these matrices on the basis of survey data gathered to capture transmission risks for respiratory diseases. We provide an overview of developments in the construction of matrices for capturing transmission opportunities in populations. Such transmission matrices are useful for epidemiologic modelling to capture within and between stratum transmission and can be informed from theoretical mixing assumptions, informed by empirical evidence gathered through investigation as well as generated on the basis of data. Links to summary measures and threshold conditions are also provided.

Black-box attacks on dynamic graphs via adversarial topology perturbations

Research and analysis of attacks on dynamic graph is beneficial for information systems to investigate vulnerabilities and strength abilities in resisting malicious attacks. Existing attacks on dynamic graphs mainly focus on rewiring original graph structures, which are often infeasible in real-world scenarios. To address this issue, we adopt a novel strategy by injecting both fake nodes and links to attack dynamic graphs. Based on that, we present the first study on attacking dynamic graphs via adversarial topology perturbations in a restricted black-box setting, in which downstream graph learning tasks are unknown. Specifically, we first divide dynamic graph structure perturbations into three sub-tasks and transform them as a sequential decision making process. Then, we propose a hierarchical reinforcement learning based black-box attack (HRBBA) framework to model three sub-tasks as attack policies. In addition, an imperceptible perturbation constraint to guarantee the concealment of attacks is incorporated into HRBBA. Finally, HRBBA is optimized based on the actor-critic process. Extensive experiments on four real-world dynamic graphs show that the performance of diverse dynamic graph learning methods (victim methods) on tasks like link prediction, node classification and network clustering can be substantially degraded under HRBBA attack.

Quality assessment and community detection methods for anonymized mobility data in the Italian Covid context

We discuss how to assess the reliability of partial, anonymized mobility data and compare two different methods to identify spatial communities based on movements: Greedy Modularity Clustering (GMC) and the novel Critical Variable Selection (CVS). These capture different aspects of mobility: direct population fluxes (GMC) and the probability for individuals to move between two nodes (CVS). As a test case, we consider movements of Italians before and during the SARS-Cov2 pandemic, using Facebook users' data and publicly available information from the Italian National Institute of Statistics (Istat) to construct daily mobility networks at the interprovincial level. Using the Perron-Frobenius (PF) theorem, we show how the mean stochastic network has a stationary population density state comparable with data from Istat, and how this ceases to be the case if even a moderate amount of pruning is applied to the network. We then identify the first two national lockdowns through temporal clustering of the mobility networks, define two representative graphs for the lockdown and non-lockdown conditions and perform optimal spatial community identification on both graphs using the GMC and CVS approaches. Despite the fundamental differences in the methods, the variation of information (VI) between them assesses that they return similar partitions of the Italian provincial networks in both situations. The information provided can be used to inform policy, for example, to define an optimal scale for lockdown measures. Our approach is general and can be applied to other countries or geographical scales.

Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs

The presence of the giant component is a necessary condition for the emergence of collective behavior in complex networked systems. Unlike networks, hypergraphs have an important native feature that components of hypergraphs might be of higher order, which could be defined in terms of the number of common nodes shared between hyperedges. Although the extensive higher-order component (HOC) could be witnessed ubiquitously in real-world hypergraphs, the role of the giant HOC in collective behavior on hypergraphs has yet to be elucidated. In this Letter, we demonstrate that the presence of the giant HOC fundamentally alters the outbreak patterns of higher-order contagion dynamics on real-world hypergraphs. Most crucially, the giant HOC is required for the higher-order contagion to invade globally from a single seed. We confirm it by using synthetic random hypergraphs containing adjustable and analytically calculable giant HOC.

Comparative approaches in social network ecology

Social systems vary enormously across the animal kingdom, with important implications for ecological and evolutionary processes such as infectious disease dynamics, anti-predator defence, and the evolution of cooperation. Comparing social network structures between species offers a promising route to help disentangle the ecological and evolutionary processes that shape this diversity. Comparative analyses of networks like these are challenging and have been used relatively little in ecology, but are becoming increasingly feasible as the number of empirical datasets expands. Here, we provide an overview of multispecies comparative social network studies in ecology and evolution. We identify a range of advancements that these studies have made and key challenges that they face, and we use these to guide methodological and empirical suggestions for future research. Overall, we hope to motivate wider publication and analysis of open social network datasets in animal ecology.

Exploring Temporal Community Structure via Network Embedding

Temporal community detection is helpful to discover and analyze significant groups or clusters hidden in dynamic networks in the real world. A variety of methods, such as modularity optimization, spectral method, and statistical network model, has been developed from diversified perspectives. Recently, network embedding-based technologies have made significant progress, and one can exploit deep learning superiority to network tasks. Although some methods for static networks have shown promising results in boosting community detection by integrating community embedding, they are not suitable for temporal networks and unable to capture their dynamics. Furthermore, the dynamic embedding methods only model network varying without considering community structures. Hence, in this article, we propose a novel unsupervised dynamic community detection model, which is based on network embedding and can effectively discover temporal communities and model dynamic networks. More specifically, we propose the community prior by introducing the Gaussian mixture model (GMM) in the variational autoencoder, which can obtain community information and better model the evolutionary characteristics of community structure and node embedding by utilizing the variant of gated recurrent unit (GRU). Extensive experiments conducted in real-world and artificial networks demonstrate that our proposed model has a better effect on improving the accuracy of dynamic community detection.

Locating community smells in software development processes using higher-order network centralities

Community smells are negative patterns in software development teams' interactions that impede their ability to successfully create software. Examples are team members working in isolation, lack of communication and collaboration across departments or sub-teams, or areas of the codebase where only a few team members can work on. Current approaches aim to detect community smells by analysing static network representations of software teams' interaction structures. In doing so, they are insufficient to locate community smells within development processes. Extending beyond the capabilities of traditional social network analysis, we show that higher-order network models provide a robust means of revealing such hidden patterns and complex relationships. To this end, we develop a set of centrality measures based on the MOGen higher-order network model and show their effectiveness in predicting influential nodes using five empirical datasets. We then employ these measures for a comprehensive analysis of a product team at the German IT security company genua GmbH, showcasing our method's success in identifying and locating community smells. Specifically, we uncover critical community smells in two areas of the team's development process. Semi-structured interviews with five team members validate our findings: while the team was aware of one community smell and employed measures to address it, it was not aware of the second. This highlights the potential of our approach as a robust tool for identifying and addressing community smells in software development teams. More generally, our work contributes to the social network analysis field with a powerful set of higher-order network centralities that effectively capture community dynamics and indirect relationships.

Hyper-cores promote localization and efficient seeding in higher-order processes

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.

Adaptive group testing strategy for infectious diseases using social contact graph partitions

Mass testing is essential for identifying infected individuals during an epidemic and allowing healthy individuals to return to normal social activities. However, testing capacity is often insufficient to meet global health needs, especially during newly emerging epidemics. Dorfman's method, a classic group testing technique, helps reduce the number of tests required by pooling the samples of multiple individuals into a single sample for analysis. Dorfman's method does not consider the time dynamics or limits on testing capacity involved in infection detection, and it assumes that individuals are infected independently, ignoring community correlations. To address these limitations, we present an adaptive group testing (AGT) strategy based on graph partitioning, which divides a physical contact network into subgraphs (groups of individuals) and assigns testing priorities based on the social contact characteristics of each subgraph. Our AGT aims to maximize the number of infected individuals detected and minimize the number of tests required. After each testing round (perhaps on a daily basis), the testing priority is increased for each neighboring group of known infected individuals. We also present an enhanced infectious disease transmission model that simulates the dynamic spread of a pathogen and evaluate our AGT strategy using the simulation results. When applied to 13 social contact networks, AGT demonstrates significant performance improvements compared to Dorfman's method and its variations. Our AGT strategy requires fewer tests overall, reduces disease spread, and retains robustness under changes in group size, testing capacity, and other parameters. Testing plays a crucial role in containing and mitigating pandemics by identifying infected individuals and helping to prevent further transmission in families and communities. By identifying infected individuals and helping to prevent further transmission in families and communities, our AGT strategy can have significant implications for public health, providing guidance for policymakers trying to balance economic activity with the need to manage the spread of infection.

Close contact behaviors of university and school students in 10 indoor environments

Close contact routes, including short-range airborne and large-droplet routes, play an important role in the transmission of SARS-CoV-2 in indoor environments. However, the exposure risk of such routes is difficult to quantify due to the lack of data on the close contact behavior of individuals. In this study, a digital wearable device, based on semi-supervised learning, was developed to automatically record human close contact behavior. We collected 337,056 s of indoor close contact of school and university students from 194.5 h of depth video recordings in 10 types of indoor environments. The correlation between aerosol exposure and close contact behaviors was then evaluated. Individuals in restaurants had the highest close contact ratio (64%), as well as the highest probability of face-to-face pattern (78%) during close contact. Accordingly, university students showed greater exposure potential in dormitories than school students in homes, however, a lower exposure was observed in classrooms and postgraduate student offices in comparison with school students in classrooms. In addition, restaurants had the highest aerosol exposure volume for both short-range inhalation and direct deposition on the facial mucosa. Thus, the classroom was established as the primary indoor environment where school students are exposed to aerosols.

Direct indicators of social distancing effectiveness in COVID-19 outbreak stages: a correlational analysis of case contacts and population mobility in Korea

OBJECTIVES

The effectiveness of social distancing during the coronavirus disease 2019 (COVID-19) pandemic has been evaluated using the magnitude of changes in population mobility. This study aimed to investigate a direct indicator-namely, the number of close contacts per patient with confirmed COVID-19.

METHODS

From week 7, 2020 to week 43, 2021, population movement changes were calculated from the data of two Korean telecommunication companies and Google in accordance with social distancing stringency levels. Data on confirmed cases and their close contacts among residents of Gyeonggi Province, Korea were combined at each stage. Pearson correlation analysis was conducted to compare the movement data with the change in the number of contacts for each confirmed case calculated by stratification according to age group. The reference value of the population movement data was set using the value before mid-February 2020, considering each data's characteristics.

RESULTS

In the age group of 18 or younger, the number of close contacts per confirmed case decreased or increased when the stringency level was strengthened or relaxed, respectively. In adults, the correlation was relatively low, with no correlation between the change in the number of close contacts per confirmed case and the change in population movement after the commencement of vaccination for adults.

CONCLUSIONS

The effectiveness of governmental social distancing policies against COVID-19 can be evaluated using the number of close contacts per confirmed case as a direct indicator, especially for each age group. Such an analysis can facilitate policy changes for specific groups.

Social connectedness at the playground before and after COVID-19 school closure

Social connectedness at school is crucial to children's development, yet very little is known about the way it has been affected by school closures during COVID-19 pandemic. We compared pre-post lockdown levels of social connectedness at a school playground in forty-three primary school-aged children, using wearable sensors, observations, peer nominations and self-reports. Upon school reopening, findings from sensors and peer nominations indicated increases in children's interaction time, network diversity and network centrality. Group observations indicated a decrease in no-play social interactions and an increase in children's involvement in social play. Explorative analyses did not reveal relations between changes in peer connectedness and pre-lockdown levels of peer connectedness or social contact during the lockdown period. Findings pointed at the role of recess in contributing to children's social well-being and the importance of attending to their social needs upon reopening.

From Ties to Events in the Analysis of Interorganizational Exchange Relations

Relational event models expand the analytical possibilities of existing statistical models for interorganizational networks by: (i) making efficient use of information contained in the sequential ordering of observed events connecting sending and receiving units; (ii) accounting for the intensity of the relation between exchange partners, and (iii) distinguishing between short- and long-term network effects. We introduce a recently developed relational event model (REM) for the analysis of continuously observed interorganizational exchange relations. The combination of efficient sampling algorithms and sender-based stratification makes the models that we present particularly useful for the analysis of very large samples of relational event data generated by interaction among heterogeneous actors. We demonstrate the empirical value of event-oriented network models in two different settings for interorganizational exchange relations-that is, high-frequency overnight transactions among European banks and patient-sharing relations within a community of Italian hospitals. We focus on patterns of direct and generalized reciprocity while accounting for more complex forms of dependence present in the data. Empirical results suggest that distinguishing between degree- and intensity-based network effects, and between short- and long-term effects is crucial to our understanding of the dynamics of interorganizational dependence and exchange relations. We discuss the general implications of these results for the analysis of social interaction data routinely collected in organizational research to examine the evolutionary dynamics of social networks within and between organizations.

Distinguishing Simple and Complex Contagion Processes on Networks

Contagion processes on networks, including disease spreading, information diffusion, or social behaviors propagation, can be modeled as simple contagion, i.e., as a contagion process involving one connection at a time, or as complex contagion, in which multiple interactions are needed for a contagion event. Empirical data on spreading processes, however, even when available, do not easily allow us to uncover which of these underlying contagion mechanisms is at work. We propose a strategy to discriminate between these mechanisms upon the observation of a single instance of a spreading process. The strategy is based on the observation of the order in which network nodes are infected, and on its correlations with their local topology: these correlations differ between processes of simple contagion, processes involving threshold mechanisms, and processes driven by group interactions (i.e., by "higher-order" mechanisms). Our results improve our understanding of contagion processes and provide a method using only limited information to distinguish between several possible contagion mechanisms.

Spatial immunization to abate disease spreading in transportation hubs

Proximity social interactions are crucial for infectious diseases transmission. Crowded agglomerations pose serious risk of triggering superspreading events. Locations like transportation hubs (airports and stations) are designed to optimize logistic efficiency, not to reduce crowding, and are characterized by a constant in and out flow of people. Here, we analyze the paradigmatic example of London Heathrow, one of the busiest European airports. Thanks to a dataset of anonymized individuals' trajectories, we can model the spreading of different diseases to localize the contagion hotspots and to propose a spatial immunization policy targeting them to reduce disease spreading risk. We also detect the most vulnerable destinations to contagions produced at the airport and quantify the benefits of the spatial immunization technique to prevent regional and global disease diffusion. This method is immediately generalizable to train, metro and bus stations and to other facilities such as commercial or convention centers.

Empirical evidence of transmission over a school-household network for SARS-CoV-2; exploration of transmission pairs stratified by primary and secondary school

BACKGROUND

Children play a key role in the transmission of many infectious diseases. They have many of their close social encounters at home or at school. We hypothesized that most of the transmission of respiratory infections among children occur in these two settings and that transmission patterns can be predicted by a bipartite network of schools and households.

AIM AND METHODS

To confirm transmission over a school-household network, SARS-CoV-2 transmission pairs in children aged 4-17 years were analyzed by study year and primary/secondary school. Cases with symptom onset between 1 March 2021 and 4 April 2021 identified by source and contact-tracing in the Netherlands were included. In this period, primary schools were open and secondary school students attended class at least once per week. Within pairs, spatial distance between the postcodes was calculated as the Euclidean distance.

RESULTS

A total of 4059 transmission pairs were identified; 51.9% between primary schoolers; 19.6% between primary and secondary schoolers; 28.5% between secondary schoolers. Most (68.5%) of the transmission for children in the same study year occurred at school. In contrast, most of the transmission of children from different study years (64.3%) and most primary-secondary transmission (81.7%) occurred at home. The average spatial distance between infections was 1.2 km (median 0.4) for primary school pairs, 1.6 km (median 0) for primary-secondary school pairs and 4.1 km (median 1.2) for secondary school pairs.

CONCLUSION

The results provide evidence of transmission on a bipartite school-household network. Schools play an important role in transmission within study years, and households play an important role in transmission between study years and between primary and secondary schools. Spatial distance between infections in a transmission pair reflects the smaller school catchment area of primary schools versus secondary schools. Many of these observed patterns likely hold for other respiratory pathogens.

Multi-layer network approach in modeling epidemics in an urban town

ABSTRACT

The last three years have been an extraordinary time with the COVID-19 pandemic killing millions, affecting and distressing billions of people worldwide. Authorities took various measures such as turning school and work to remote and prohibiting social relations via curfews. In order to mitigate the negative impact of the epidemics, researchers tried to estimate the future of the pandemic for different scenarios, using forecasting techniques and epidemics simulations on networks. Intending to better represent the real-life in an urban town in high resolution, we propose a novel multi-layer network model, where each layer corresponds to a different interaction that occurs daily, such as "household", "work" or "school". Our simulations indicate that locking down "friendship" layer has the highest impact on slowing down epidemics. Hence, our contributions are twofold, first we propose a parametric network generator model; second, we run SIR simulations on it and show the impact of layers.

Minimising school disruption under high incidence conditions due to the Omicron variant in France, Switzerland, Italy, in January 2022

BackgroundAs record cases of Omicron variant were registered in Europe in early 2022, schools remained a vulnerable setting undergoing large disruption.AimThrough mathematical modelling, we compared school protocols of reactive screening, regular screening, and reactive class closure implemented in France, in Baselland (Switzerland), and in Italy, respectively, and assessed them in terms of case prevention, testing resource demand, and schooldays lost.MethodsWe used a stochastic agent-based model of SARS-CoV-2 transmission in schools accounting for within- and across-class contacts from empirical contact data. We parameterised it to the Omicron BA.1 variant to reproduce the French Omicron wave in January 2022. We simulated the three protocols to assess their costs and effectiveness for varying peak incidence rates in the range experienced by European countries.ResultsWe estimated that at the high incidence rates registered in France during the Omicron BA.1 wave in January 2022, the reactive screening protocol applied in France required higher test resources compared with the weekly screening applied in Baselland (0.50 vs 0.45 tests per student-week), but achieved considerably lower control (8% vs 21% reduction of peak incidence). The reactive class closure implemented in Italy was predicted to be very costly, leading to > 20% student-days lost.ConclusionsAt high incidence conditions, reactive screening protocols generate a large and unplanned demand in testing resources, for marginal control of school transmissions. Comparable or lower resources could be more efficiently used through weekly screening. Our findings can help define incidence levels triggering school protocols and optimise their cost-effectiveness.

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.

Contact networks have small metric backbones that maintain community structure and are primary transmission subgraphs

The structure of social networks strongly affects how different phenomena spread in human society, from the transmission of information to the propagation of contagious diseases. It is well-known that heterogeneous connectivity strongly favors spread, but a precise characterization of the redundancy present in social networks and its effect on the robustness of transmission is still lacking. This gap is addressed by the metric backbone, a weight- and connectivity-preserving subgraph that is sufficient to compute all shortest paths of weighted graphs. This subgraph is obtained via algebraically-principled axioms and does not require statistical sampling based on null-models. We show that the metric backbones of nine contact networks obtained from proximity sensors in a variety of social contexts are generally very small, 49% of the original graph for one and ranging from about 6% to 20% for the others. This reflects a surprising amount of redundancy and reveals that shortest paths on these networks are very robust to random attacks and failures. We also show that the metric backbone preserves the full distribution of shortest paths of the original contact networks-which must include the shortest inter- and intra-community distances that define any community structure-and is a primary subgraph for epidemic transmission based on pure diffusion processes. This suggests that the organization of social contact networks is based on large amounts of shortest-path redundancy which shapes epidemic spread in human populations. Thus, the metric backbone is an important subgraph with regard to epidemic spread, the robustness of social networks, and any communication dynamics that depend on complex network shortest paths.

Impact of human contact patterns on epidemic spreading in time-varying networks

Human contact behaviors involve both dormant and active processes. The dormant (active) process goes from the disappearance (creation) to the creation (disappearance) of an edge. The dormant (active) time is the elapsed time since the edge became dormant (active). Many empirical studies have revealed that dormant and active times in human contact behaviors tend to show a long-tailed distribution. Previous researches focused on the impact of the dormant process on spreading dynamics. However, the epidemic spreading happens on the active process. This raises the question of how the active process affects epidemic spreading in complex networks. Here, we propose a novel time-varying network model in which the distributions of both the dormant time and active time of edges are adjustable. We develop a pairwise approximation method to describe the spreading dynamical processes in the time-varying networks. Through extensive numerical simulations, we find that the epidemic threshold is proportional to the mean dormant time and inversely proportional to the mean active time. The attack rate decreases with the increase of mean dormant time and increases with the increase of mean active time. It is worth noting that the epidemic threshold and the attack rate (e.g., the infected density in the steady state) are independent of the heterogeneities of the dormant time distribution and the active time distribution. Increasing the heterogeneity of the dormant time distribution accelerates epidemic spreading while increasing the heterogeneity of the active time distribution slows it down.

Generative hypergraph models and spectral embedding

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into low-dimensional Euclidean space so that most interactions are short-range. This embedding is relevant to many follow-on tasks, such as node reordering, clustering, and visualization. We focus on two spectral embedding algorithms customized to hypergraphs which recover linear and periodic structures respectively. In the periodic case, nodes are positioned on the unit circle. We show that the two spectral hypergraph embedding algorithms are associated with a new class of generative hypergraph models. These models generate hyperedges according to node positions in the embedded space and encourage short-range connections. They allow us to quantify the relative presence of periodic and linear structures in the data through maximum likelihood. They also improve the interpretability of node embedding and provide a metric for hyperedge prediction. We demonstrate the hypergraph embedding and follow-on tasks-including quantifying relative strength of structures, clustering and hyperedge prediction-on synthetic and real-world hypergraphs. We find that the hypergraph approach can outperform clustering algorithms that use only dyadic edges. We also compare several triadic edge prediction methods on high school and primary school contact hypergraphs where our algorithm improves upon benchmark methods when the amount of training data is limited.

Combinatorial characterizations and impossibilities for higher-order homophily

Homophily is the seemingly ubiquitous tendency for people to connect and interact with other individuals who are similar to them. This is a well-documented principle and is fundamental for how society organizes. Although many social interactions occur in groups, homophily has traditionally been measured using a graph model, which only accounts for pairwise interactions involving two individuals. Here, we develop a framework using hypergraphs to quantify homophily from group interactions. This reveals natural patterns of group homophily that appear with gender in scientific collaboration and political affiliation in legislative bill cosponsorship and also reveals distinctive gender distributions in group photographs, all of which cannot be fully captured by pairwise measures. At the same time, we show that seemingly natural ways to define group homophily are combinatorially impossible. This reveals important pitfalls to avoid when defining and interpreting notions of group homophily, as higher-order homophily patterns are governed by combinatorial constraints that are independent of human behavior but are easily overlooked.

Longitudinal data collection to follow social network and language development dynamics at preschool

DyLNet is a large-scale longitudinal social experiment designed to observe the relations between child socialisation and oral language learning at preschool. During three years, a complete preschool in France was followed to record proximity interactions of about 200 children and adults every 5 seconds using autonomous Radio Frequency Identification Wireless Proximity Sensors. Data was collected monthly with one week-long deployments. In parallel, survey campaigns were carried out to record the socio-demographic and language background of children and their families, and to monitor the linguistic skills of the pupils at regular intervals. From data we inferred real social interactions and distinguished inter- and intra-class interactions in different settings. We share ten weeks of cleaned, pre-processed and reconstructed interaction data recorded over a complete school year, together with two sets of survey data providing details about the pupils' socio-demographic profile and language development level at the beginning and end of this period. Our dataset may stimulate researchers from several fields to study the simultaneous development of language and social interactions of children.

Modularity, balance, and frustration in student social networks: The role of negative relationships in communities

Signed networks provide information to study the structure and composition of relationships (positive and negative) among individuals in a complex system. Individuals, through different criteria, form groups or organizations called communities. Community structures are one of the important properties of social networks. In this work, we aim to analyze the perturbation of negative relationships in communities. We developed a methodology to obtain and analyze the optimal community partitions in nine school networks in the state of Yucatán, México. We implemented a technique based on the social balance theory in signed networks to complete negative missing links and further applied two methods of community detection: Newman's and Louvain's algorithms. We obtain values close to Dunbar's ratio for both types of relationships, positive and negative. The concepts of balance and frustration were analyzed, and modularity was used to measure the perturbation of negative relationships in communities. We observe differences among communities of different academic degrees. Elementary school communities are unstable, i.e. significantly perturbed by negative relationships, in secondary school communities are semi-stable, and in high school and the university the communities are stable. The analyzes indicate that a greater number of negative links in the networks does not necessarily imply higher instability in the communities, but other social factors are also involved.

Dynamics of cold random hyperbolic graphs with link persistence

We consider and analyze a dynamic model of random hyperbolic graphs with link persistence. In the model, both connections and disconnections can be propagated from the current to the next snapshot with probability ω∈[0,1). Otherwise, with probability 1-ω, connections are reestablished according to the random hyperbolic graphs model. We show that while the persistence probability ω affects the averages of the contact and intercontact distributions, it does not affect the tails of these distributions, which decay as power laws with exponents that do not depend on ω. We also consider examples of real temporal networks, and we show that the considered model can adequately reproduce several of their dynamical properties. Our results advance our understanding of the realistic modeling of temporal networks and of the effects of link persistence on temporal network properties.

$$\Delta $$-Conformity: multi-scale node assortativity in feature-rich stream graphs

Multi-scale strategies to estimate mixing patterns are meant to capture heterogeneous behaviors among node homophily, but they ignore an important addendum often available in real-world networks: the time when edges are present and the time-varying paths that edges form accordingly. In this work, we go beyond the assumption of a static network topology to propose a multi-scale, path- and time-aware node homophily estimator specifically tied for feature-rich stream graphs: $$\Delta $$ Δ -Conformity. Our measure can capture the homogeneous/heterogeneous tendency of nodes’ connectivity along a period of time $$\Delta $$ Δ starting from a given moment in time. Results on face-to-face interaction networks suggest it is possible to track changes in social mixing behaviors that coincide with contextually reasonable everyday patterns, e.g., medical staff disassortative behavior when exposed to patients. In a different domain, that of the Bitcoin Transaction Network, we capture relationships between the quantity of money sent from (and to) different categories/continents and their respective mixing trends over time. All these insights help us to introduce $$\Delta $$ Δ -Conformity as a suitable solution for understanding temporal homophily by capturing the mixing tendency of entities embedded in fine-grained evolving contexts.

Inference of hyperedges and overlapping communities in hypergraphs

Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions. Furthermore, our model has an efficient numerical implementation, and it runs faster than dyadic algorithms on pairwise records projected from higher-order data. We apply our method to a variety of real-world systems, showing strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness against addition of noisy hyperedges. Our approach illustrates the fundamental advantages of a hypergraph probabilistic model when modeling relational systems with higher-order interactions.

Data mining methodology for obtaining epidemiological data in the context of road transport systems

Millions of people use public transport systems daily, hence their interest for the epidemiology of respiratory infectious diseases, both from a scientific and a health control point of view. This article presents a methodology for obtaining epidemiological information on these types of diseases in the context of a public road transport system. This epidemiological information is based on an estimation of interactions with risk of infection between users of the public transport system. The methodology is novel in its aim since, to the best of our knowledge, there is no previous study in the context of epidemiology and public transport systems that addresses this challenge. The information is obtained by mining the data generated from trips made by transport users who use contactless cards as a means of payment. Data mining therefore underpins the methodology. One achievement of the methodology is that it is a comprehensive approach, since, starting from a formalisation of the problem based on epidemiological concepts and the transport activity itself, all the necessary steps to obtain the required epidemiological knowledge are described and implemented. This includes the estimation of data that are generally unknown in the context of public transport systems, but that are required to generate the desired results. The outcome is useful epidemiological data based on a complete and reliable description of all estimated potentially infectious interactions between users of the transport system. The methodology can be implemented using a variety of initial specifications: epidemiological, temporal, geographic, inter alia. Another feature of the methodology is that with the information it provides, epidemiological studies can be carried out involving a large number of people, producing large samples of interactions obtained over long periods of time, thereby making it possible to carry out comparative studies. Moreover, a real use case is described, in which the methodology is applied to a road transport system that annually moves around 20 million passengers, in a period that predates the COVID-19 pandemic. The results have made it possible to identify the group of users most exposed to infection, although they are not the largest group. Finally, it is estimated that the application of a seat allocation strategy that minimises the risk of infection reduces the risk by 50%.

Network Comparison with Interpretable Contrastive Network Representation Learning

Identifying unique characteristics in a network through comparison with another network is an essential network analysis task. For example, with networks of protein interactions obtained from normal and cancer tissues, we can discover unique types of interactions in cancer tissues. This analysis task could be greatly assisted by contrastive learning, which is an emerging analysis approach to discover salient patterns in one dataset relative to another. However, existing contrastive learning methods cannot be directly applied to networks as they are designed only for high-dimensional data analysis. To address this problem, we introduce a new analysis approach called contrastive network representation learning (cNRL). By integrating two machine learning schemes, network representation learning and contrastive learning, cNRL enables embedding of network nodes into a low-dimensional representation that reveals the uniqueness of one network compared to another. Within this approach, we also design a method, named i-cNRL, which offers interpretability in the learned results, allowing for understanding which specific patterns are only found in one network. We demonstrate the effectiveness of i-cNRL for network comparison with multiple network models and real-world datasets. Furthermore, we compare i-cNRL and other potential cNRL algorithm designs through quantitative and qualitative evaluations.

Effective submodularity of influence maximization on temporal networks

We study influence maximization on temporal networks. This is a special setting where the influence function is not submodular, and there is no optimality guarantee for solutions achieved via greedy optimization. We perform an exhaustive analysis on both real and synthetic networks. We show that the influence function of randomly sampled sets of seeds often violates the necessary conditions for submodularity. However, when sets of seeds are selected according to the greedy optimization strategy, the influence function behaves effectively as a submodular function. Specifically, violations of the necessary conditions for submodularity are never observed in real networks, and only rarely in synthetic ones. The direct comparison with exact solutions obtained via brute-force search indicates that the greedy strategy provides approximate solutions that are well within the optimality gap guaranteed for strictly submodular functions. Greedy optimization appears, therefore, to be an effective strategy for the maximization of influence on temporal networks.

Epidemiological, virological and serological investigation of a SARS-CoV-2 outbreak (Alpha variant) in a primary school: A prospective longitudinal study

Objectives

To report a prospective epidemiological, virological and serological investigation of a SARS-CoV-2 outbreak in a primary school.

Methods

As part of a longitudinal, prospective, school-based surveillance study, this investigation involved repeated testing of 73 pupils, 9 teachers, 13 non-teaching staff and 26 household members of participants who tested positive, with rapid antigen tests and/or RT-PCR (Day 0–2 and Day 5–7), serologies on dried capillary blood samples (Day 0–2 and Day 30), contact tracing interviews and SARS-CoV-2 whole genome sequencing.

Results

We identified 20 children (aged 4 to 6 years from 4 school classes), 2 teachers and a total of 4 household members who were infected by the Alpha variant during this outbreak. Infection attack rates were between 11.8 and 62.0% among pupils from the 4 school classes, 22.2% among teachers and 0% among non-teaching staff. Secondary attack rate among household members was 15.4%. Symptoms were reported by 63% of infected children, 100% of teachers and 50% of household members. All analysed sequences but one showed 100% identity. Serological tests detected 8 seroconversions unidentified by SARS-CoV-2 virological tests.

Conclusions

This study confirmed child-to-child and child-to-adult SARS-CoV-2 transmission and introduction into households. Effective measures to limit transmission in schools have the potential to reduce the overall community circulation.

Direct assessment of overnight parent-child proximity in children with behavioral insomnia: Extending models of operant and classical conditioning

INTRODUCTION

Explanatory models of behavioral insomnia typically draw on operant learning theory with behavioral techniques focused on altering parent-child interactions to improve sleep. However, there are no data describing parent-child interactions overnight beyond parent report. In this study we used radio frequency identification technology to quantify parent-child proximity overnight in two groups at elevated risk of behavioral insomnia, Angelman syndrome (AS) and Smith-Magenis syndrome (SMS).

MATERIALS AND METHODS

Nineteen children aged 4-15 years (8 with AS, 11 with SMS) participated in a week-long at-home assessment of sleep and overnight parent-child proximity. Sleep parameters were recorded using the Philips Actiwatch 2 and proximity data were recorded using custom-built radio frequency identification watches.

RESULTS

Three patterns of proximity data between parent-child dyads overnight were evident: "checking" (six with AS, five with SMS), "co-sleeping" (four with SMS) and those who had "no proximity" overnight (two with AS, two with SMS). In the AS group, 25.45% of actigraphy-defined wakes resulted in a parent-child interaction. In the SMS group, 39.34% of wakes resulted in a parent-child interaction. Children who interacted with their parents when settling to sleep were not significantly more likely to interact at waking.

DISCUSSION

The novel application of radio frequency identification technology is a feasible method for studying overnight parent-child proximity. Profiles of proximity between participants that are not closely aligned with operant models of behavioral insomnia were evident. These results have significant implications for the etiology of poor sleep and the application of behavioral sleep interventions.

Screening and vaccination against COVID-19 to minimise school closure: a modelling study

BACKGROUND

Schools were closed extensively in 2020-21 to counter SARS-CoV-2 spread, impacting students' education and wellbeing. With highly contagious variants expanding in Europe, safe options to maintain schools open are urgently needed. By estimating school-specific transmissibility, our study evaluates costs and benefits of different protocols for SARS-CoV-2 control at school.

METHODS

We developed an agent-based model of SARS-CoV-2 transmission in schools. We used empirical contact data in a primary and a secondary school and data from pilot screenings in 683 schools during the alpha variant (B.1.1.7) wave in March-June, 2021, in France. We fitted the model to observed school prevalence to estimate the school-specific effective reproductive number for the alpha (Ralpha) and delta (B.1.617.2; Rdelta) variants and performed a cost-benefit analysis examining different intervention protocols.

FINDINGS

We estimated Ralpha to be 1·40 (95% CI 1·35-1·45) in the primary school and 1·46 (1·41-1·51) in the secondary school during the spring wave, higher than the time-varying reproductive number estimated from community surveillance. Considering the delta variant and vaccination coverage in Europe as of mid-September, 2021, we estimated Rdelta to be 1·66 (1·60-1·71) in primary schools and 1·10 (1·06-1·14) in secondary schools. Under these conditions, weekly testing of 75% of unvaccinated students (PCR tests on saliva samples in primary schools and lateral flow tests in secondary schools), in addition to symptom-based testing, would reduce cases by 34% (95% CI 32-36) in primary schools and 36% (35-39) in secondary schools compared with symptom-based testing alone. Insufficient adherence was recorded in pilot screening (median ≤53%). Regular testing would also reduce student-days lost up to 80% compared with reactive class closures. Moderate vaccination coverage in students would still benefit from regular testing for additional control-ie, weekly testing 75% of unvaccinated students would reduce cases compared with symptom-based testing only, by 23% in primary schools when 50% of children are vaccinated.

INTERPRETATION

The COVID-19 pandemic will probably continue to pose a risk to the safe and normal functioning of schools. Extending vaccination coverage in students, complemented by regular testing with good adherence, are essential steps to keep schools open when highly transmissible variants are circulating.

FUNDING

EU Framework Programme for Research and Innovation Horizon 2020, Horizon Europe Framework Programme, Agence Nationale de la Recherche, ANRS-Maladies Infectieuses Émergentes.

Targeting attack hypergraph networks

In modern systems, from brain neural networks to social group networks, pairwise interactions are not sufficient to express higher-order relationships. The smallest unit of their internal function is not composed of a single functional node but results from multiple functional nodes acting together. Therefore, researchers adopt the hypergraph to describe complex systems. The targeted attack on random hypergraph networks is still a problem worthy of study. This work puts forward a theoretical framework to analyze the robustness of random hypergraph networks under the background of a targeted attack on nodes with high or low hyperdegrees. We discovered the process of cascading failures and the giant connected cluster (GCC) of the hypergraph network under targeted attack by associating the simple mapping of the factor graph with the hypergraph and using percolation theory and generating function. On random hypergraph networks, we do Monte-Carlo simulations and find that the theoretical findings match the simulation results. Similarly, targeted attacks are more effective than random failures in disintegrating random hypergraph networks. The threshold of the hypergraph network grows as the probability of high hyperdegree nodes being deleted increases, indicating that the network's resilience becomes more fragile. When considering real-world scenarios, our conclusions are validated by real-world hypergraph networks. These findings will help us understand the impact of the hypergraph's underlying structure on network resilience.

Full reconstruction of simplicial complexes from binary contagion and Ising data

Previous efforts on data-based reconstruction focused on complex networks with pairwise or two-body interactions. There is a growing interest in networks with higher-order or many-body interactions, raising the need to reconstruct such networks based on observational data. We develop a general framework combining statistical inference and expectation maximization to fully reconstruct 2-simplicial complexes with two- and three-body interactions based on binary time-series data from two types of discrete-state dynamics. We further articulate a two-step scheme to improve the reconstruction accuracy while significantly reducing the computational load. Through synthetic and real-world 2-simplicial complexes, we validate the framework by showing that all the connections can be faithfully identified and the full topology of the 2-simplicial complexes can be inferred. The effects of noisy data or stochastic disturbance are studied, demonstrating the robustness of the proposed framework.

Data-driven recovery of topology is challenging for networks beyond pairwise interactions. The authors propose a framework to reconstruct complex networks with higher-order interactions from time series, focusing on networks with 2-simplexes where social contagion and Ising dynamics generate binary data.

Impact of contact data resolution on the evaluation of interventions in mathematical models of infectious diseases

Computational models offer a unique setting to test strategies to mitigate the spread of infectious diseases, providing useful insights to applied public health. To be actionable, models need to be informed by data, which can be available at different levels of detail. While high-resolution data describing contacts between individuals are increasingly available, data gathering remains challenging, especially during a health emergency. Many models thus use synthetic data or coarse information to evaluate intervention protocols. Here, we evaluate how the representation of contact data might affect the impact of various strategies in models, in the realm of COVID-19 transmission in educational and work contexts. Starting from high-resolution contact data, we use detailed to coarse data representations to inform a model of SARS-CoV-2 transmission and simulate different mitigation strategies. We find that coarse data representations estimate a lower risk of superspreading events. However, the rankings of protocols according to their efficiency or cost remain coherent across representations, ensuring the consistency of model findings to inform public health advice. Caution should be taken, however, on the quantitative estimations of those benefits and costs triggering the adoption of protocols, as these may depend on data representation.

Time-varying graph representation learning via higher-order skip-gram with negative sampling

Representation learning models for graphs are a successful family of techniques that project nodes into feature spaces that can be exploited by other machine learning algorithms. Since many real-world networks are inherently dynamic, with interactions among nodes changing over time, these techniques can be defined both for static and for time-varying graphs. Here, we show how the skip-gram embedding approach can be generalized to perform implicit tensor factorization on different tensor representations of time-varying graphs. We show that higher-order skip-gram with negative sampling (HOSGNS) is able to disentangle the role of nodes and time, with a small fraction of the number of parameters needed by other approaches. We empirically evaluate our approach using time-resolved face-to-face proximity data, showing that the learned representations outperform state-of-the-art methods when used to solve downstream tasks such as network reconstruction. Good performance on predicting the outcome of dynamical processes such as disease spreading shows the potential of this method to estimate contagion risk, providing early risk awareness based on contact tracing data.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1140/epjds/s13688-022-00344-8.

Flow stability for dynamic community detection

Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in these systems is to extract a simplified view of their time-dependent network of interactions. Community detection in temporal networks usually relies on aggregation over time windows or consider sequences of different stationary epochs. For dynamics-based methods, attempts to generalize static-network methodologies also face the fundamental difficulty that a stationary state of the dynamics does not always exist. Here, we derive a method based on a dynamical process evolving on the temporal network. Our method allows dynamics that do not reach a steady state and uncovers two sets of communities for a given time interval that accounts for the ordering of edges in forward and backward time. We show that our method provides a natural way to disentangle the different dynamical scales present in a system with synthetic and real-world examples.

Modular reactivation of Mexico City after COVID-19 lockdown

BACKGROUND

During the COVID-19 pandemic, the slope of the epidemic curve in Mexico City has been quite unstable. Changes in human activity led to changes in epidemic activity, hampering attempts at economic and general reactivation of the city.

METHODS

We have predicted that where a fraction of the population above a certain threshold returns to the public space, the negative tendency of the epidemic curve will revert. Such predictions were based on modeling the reactivation of economic activity after lockdown using an epidemiological model resting upon a contact network of Mexico City derived from mobile device co-localization. We modeled scenarios with different proportions of the population returning to normalcy. Null models were built using the Jornada Nacional de Sana Distancia (the Mexican model of elective lockdown). There was a mobility reduction of 75% and no mandatory mobility restrictions.

RESULTS

We found that a new peak of cases in the epidemic curve was very likely for scenarios in which more than 5% of the population rejoined the public space. The return of more than 50% of the population synchronously will unleash a magnitude similar to the one predicted with no mitigation strategies. By evaluating the tendencies of the epidemic dynamics, the number of new cases registered, hospitalizations, and recent deaths, we consider that reactivation following only elective measures may not be optimal under this scenario.

CONCLUSIONS

Given the need to resume economic activities, we suggest alternative measures that minimize unnecessary contacts among people returning to the public space. We evaluated that "encapsulating" reactivated workers (that is, using measures to reduce the number of contacts beyond their influential community in the contact network) may allow reactivation of a more significant fraction of the population without compromising the desired tendency in the epidemic curve.

Hidden dependence of spreading vulnerability on topological complexity

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time-commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its "spreading vulnerability," is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the "entropy of temporal entanglement" as a quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological, and engineered systems.

Directed percolation in random temporal network models with heterogeneities

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similarly to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and, otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low-dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limited-time reachability of temporal networks.

Systematic assessment of the quality of fit of the stochastic block model for empirical networks

We perform a systematic analysis of the quality of fit of the stochastic block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We employ posterior predictive model checking as a criterion to assess the quality of fit, which involves comparing networks generated by the inferred model with the empirical network, according to a set of network descriptors. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements. In particular, networks possessing a large diameter and slow-mixing random walks tend to be badly described by the SBM. However, contrary to what is often assumed, networks with a high abundance of triangles can be well described by the SBM in many cases. We demonstrate that simple network descriptors can be used to evaluate whether or not the SBM can provide a sufficiently accurate representation, potentially pointing to possible model extensions that can systematically improve the expressiveness of this class of models.