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Global and regional integration has grown significantly in recent decades, boosting intra-African trade and positively impacting national economies through trade diversification and sustainable development. However, existing measures of economic integration often fail to capture the complex interactions among trading partners. This study addresses this gap by using complex network analysis and dynamic panel regression techniques to identify factors driving economic integration in Africa, based on data from 2002 to 2019. The results show that economic development, institutional quality, regional trade agreements, human capital, FDI, and infrastructure positively influence a country's position in the African trade network. Conversely, trade costs, the global financial crisis, and regional overlapping memberships negatively affect network based integration. Our findings suggest that enhancing a country's connectivity in the African trade network involves identifying key economic and institutional factors of trade partners and strategically focusing on continent-wide agreements rather than just regional ones to boost economic growth., Comment: Comments welcome

Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey we provide an overview of the graph randomization methods available in the most popular software tools for network analysis. We propose a comparative analysis of popular software tools to highlight their functionalities and limitations. Through case studies involving diverse graph types, we demonstrate how different randomization methods can lead to divergent conclusions, emphasizing the importance of careful method selection based on the characteristics of the observed network and the research question at hand. This survey proposes some guidelines for researchers and practitioners seeking to understand and utilize graph randomization techniques effectively in their network analysis projects., Comment: 32 pages, 11 figures, 1 annex

The course of an epidemic is not only shaped by infection transmission over face-to-face contacts, but also by preventive behaviour caused by risk perception and social interactions. This study explores the dynamics of coupled awareness and biological infection spread within a two-layer multiplex network framework. One layer embodies face-to-face contacts, with a biological infection transmission following a simple contagion model, the SIR process. Awareness, modelled by the linear threshold model, a complex contagion, spreads over a social layer and induces behaviour that lowers the chance of a biological infection occurring. It may be provoked by the presence of either aware or infectious neighbours. We introduce a novel model combining these influences through a convex combination, creating a continuum between pure social contagion and local risk perception. Simulation of the model shows distinct effects arising from the awareness sources. Also, for convex combinations where both input sources are of importance, awareness cascades that are not attributable to only one of these sources, emerge. Under these conditions, the combination of a small-world face-to-face and a scale-free social layer, but not vice versa, make that the extent of the infections decreases with increasing transmission probability., Comment: 15 pages, 25 subfigures in 8 figures

Public opinion is subject to peer interaction via social networks and external pressure from the media, advertising, and other actors. In this paper, we study the interaction between external and peer influence on the stochastic opinion dynamics of a majority vote model. We introduce a model where agents update their opinions based on the combined influence of their local neighbourhood (peers) and an external actor in the transition rates. In the first model, the external influence is only felt by agents non-aligned with the external actor ("push strategy"). In the second model, agents are affected by external influence, independently of their opinions ("nudging strategy"). In both cases, the external influence increases the possible macroscopic outcomes. These outcomes are determined by the chosen influence strategy. We also find that the social network structure affects the opinion dynamics, with social clustering positively reinforcing the external influence whereas degree heterogeneity weakens the external forces. These findings are relevant to businesses and policy making, helping to understand how groups of individuals collectively react to external actors.

Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a model based on the quantum walk algorithm are compared with those obtained from classical methodologies. We focus on specific limitations of the classical models, and illustrate that the quantum walk model possesses great flexibility in overcoming these. This includes the potential to generate asymmetric return distributions with complex market tendencies and higher probabilities for extreme events than in some of the classical models. Furthermore, the temporal evolution in the quantum walk possesses the potential to provide asset price dynamics., Comment: 23 pages, 8 figures, 2 tables

Temporal (or time-evolving) networks are commonly used to model complex systems and the evolution of their components throughout time. Although these networks can be analyzed by different means, visual analytics stands out as an effective way for a pre-analysis before doing quantitative/statistical analyses to identify patterns, anomalies, and other behaviors in the data, thus leading to new insights and better decision-making. However, the large number of nodes, edges, and/or timestamps in many real-world networks may lead to polluted layouts that make the analysis inefficient or even infeasible. In this paper, we propose LargeNetVis, a web-based visual analytics system designed to assist in analyzing small and large temporal networks. It successfully achieves this goal by leveraging three taxonomies focused on network communities to guide the visual exploration process. The system is composed of four interactive visual components: the first (Taxonomy Matrix) presents a summary of the network characteristics, the second (Global View) gives an overview of the network evolution, the third (a node-link diagram) enables community- and node-level structural analysis, and the fourth (a Temporal Activity Map -- TAM) shows the community- and node-level activity under a temporal perspective., Comment: 11 pages, 9 figures

Vaccines are promising tools to control the spread of COVID-19. An effective vaccination campaign requires government policies and community engagement, sharing experiences for social support, and voicing concerns to vaccine safety and efficiency. The increasing use of online social platforms allows us to trace large-scale communication and infer public opinion in real-time. We collected more than 100 million vaccine-related tweets posted by 8 million users and used the Latent Dirichlet Allocation model to perform automated topic modeling of tweet texts during the vaccination campaign in Japan. We identified 15 topics grouped into 4 themes on Personal issue, Breaking news, Politics, and Conspiracy and humour. The evolution of the popularity of themes revealed a shift in public opinion, initially sharing the attention over personal issues (individual aspect), collecting information from the news (knowledge acquisition), and government criticisms, towards personal experiences once confidence in the vaccination campaign was established. An interrupted time series regression analysis showed that the Tokyo Olympic Games affected public opinion more than other critical events but not the course of the vaccination. Public opinion on politics was significantly affected by various events, positively shifting the attention in the early stages of the vaccination campaign and negatively later. Tweets about personal issues were mostly retweeted when the vaccination reached the younger population. The associations between the vaccination campaign stages and tweet themes suggest that the public engagement in the social platform contributed to speedup vaccine uptake by reducing anxiety via social learning and support.

Innovation is fundamental for development and provides a competitive advantage for societies. It is the process of creating more complex technologies, ideas, or protocols from existing ones. While innovation may be created by single agents (i.e. individuals or organisations), it is often a result of social interactions between agents exchanging and combining complementary expertise and perspectives. The structure of social networks impacts this knowledge exchange process. To study the role of social network structures on the creation of new technologies, we design an evolutionary mechanistic model combining self-creation and social learning. We find that social heterogeneity allows agents to leverage the benefits of diversity and to develop technologies of higher complexity. Social heterogeneity, however, reduces the group ability to innovate. Not only the social structure but also the openness of agents to collaborate affect innovation. We find that interdisciplinary interactions lead to more complex technologies benefiting the entire group but also increase the inequality in the innovation output. Lower openness to interdisciplinary collaborations may be compensated by a higher ability to collaborate with multiple peers, but low openness also neutralises the intrinsic benefits of network heterogeneity. Our findings indicate that social network heterogeneity has contrasting effects on microscopic (local) and macroscopic (group) levels, suggesting that the emergence of innovation leaders may suppress the overall group performance.

Differences in the social and economic environment across countries encourage humans to migrate in search of better living conditions, including job opportunities, higher salaries, security and welfare. Quantifying global migration is, however, challenging because of poor recording, privacy issues and residence status. This is particularly critical for some classes of migrants involved in stigmatised, unregulated or illegal activities. Escorting services or high-end prostitution are well-paid activities that attract workers all around the world. In this paper, we study international migration patterns of sex-workers by using network methods. Using an extensive international online advertisement directory of escorting services and information about individual escorts, we reconstruct a migrant flow network where nodes represent either origin or destination countries. The links represent the direct routes between two countries. The migration network of sex-workers shows different structural patterns than the migration of the general population. The network contains a strong core where mutual migration is often observed between a group of high-income European countries, yet Europe is split into different network communities with specific ties to non-European countries. We find non-reciprocal relations between countries, with some of them mostly offering while others attract workers. The GDP per capita is a good indicator of country attractiveness for incoming workers and service rates but is unrelated to the probability of emigration. The median financial gain of migrating, in comparison to working at the home country, is 15.9%. Only sex-workers coming from 77% of the countries have financial gains with migration and average gains decrease with the GDPc of the country of origin. Our results shows that high-end sex-worker migration is regulated by economic, geographic and cultural aspects., Comment: Comments and feedback welcomed. Two tables and 6 figures including SI

Social animals self-organise to create groups to increase protection against predators and productivity. One-to-one interactions are the building blocks of these emergent social structures and may correspond to friendship, grooming, communication, among other social relations. These structures should be robust to failures and provide efficient communication to compensate the costs of forming and maintaining the social contacts but the specific purpose of each social interaction regulates the evolution of the respective social networks. We collate 611 animal social networks and show that the number of social contacts $E$ scales with group size $N$ as a super-linear power-law $E=CN^{\beta}$ for various species of animals, including humans, other mammals and non-mammals. We identify that the power-law exponent $\beta$ varies according to the social function of the interactions as $\beta = 1+a/4$, with $a \approx {1,2,3,4}$. By fitting a multi-layer model to our data, we observe that the cost to cross social groups also varies according to social function. Relatively low costs are observed for physical contact, grooming and group membership which lead to small groups with high and constant social clustering. Offline friendship has similar patterns while online friendship shows weak social structures. The intermediate case of spatial proximity ($\beta=1.5$ and clustering dependency on network size quantitatively similar to friendship) suggests that proximity interactions may be as relevant for the spread of infectious diseases as for social processes like friendship., Comment: To appear in Scientific Reports

Modern technology has drastically changed the way we interact and consume information. For example, online social platforms allow for seamless communication exchanges at an unprecedented scale. However, we are still bounded by cognitive and temporal constraints. Our attention is limited and extremely valuable. Algorithmic personalisation has become a standard approach to tackle the information overload problem. As result, the exposure to our friends' opinions and our perception about important issues might be distorted. However, the effects of algorithmic gatekeeping on our hyper-connected society are poorly understood. Here, we devise an opinion dynamics model where individuals are connected through a social network and adopt opinions as function of the view points they are exposed to. We apply various filtering algorithms that select the opinions shown to users i) at random ii) considering time ordering or iii) their current beliefs. Furthermore, we investigate the interplay between such mechanisms and crucial features of real networks. We found that algorithmic filtering might influence opinions' share and distributions, especially in case information is biased towards the current opinion of each user. These effects are reinforced in networks featuring topological and spatial correlations where echo chambers and polarisation emerge. Conversely, heterogeneity in connectivity patterns reduces such tendency. We consider also a scenario where one opinion, through nudging, is centrally pushed to all users. Interestingly, even minimal nudging is able to change the status quo moving it towards the desired view point. Our findings suggest that simple filtering algorithms might be powerful tools to regulate opinion dynamics taking place on social networks

Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is that they are sampled within temporal and spatial frames. Furthermore, one might wish to subsample networks to reduce their size for better visualization or to perform computationally intensive simulations. The sampling method may affect the network structure and thus caution is necessary to generalize results based on samples. In this paper, we study four sampling strategies applied to a variety of real-life temporal networks. We quantify the biases generated by each sampling strategy on a number of relevant statistics such as link activity, temporal paths and epidemic spread. We find that some biases are common in a variety of networks and statistics, but one strategy, uniform sampling of nodes, shows improved performance in most scenarios. Our results help researchers to better design network data collection protocols and to understand the limitations of sampled temporal network data., Comment: 10 pages, 8 figures, comments welcome

We investigate the impact of misinformation about the contact structure on the ability to predict disease outbreaks. We base our study on 31 empirical temporal networks and tune the frequencies in errors in the node identities or timestamps of contacts. We find that for both these spreading scenarios, the maximal misprediction of both the outbreak size and time to extinction follows an stretched exponential convergence as a function of the error frequency. We furthermore determine the temporal-network structural factors influencing the parameters of this convergence.

The Syrian civil war has been ongoing since 2011 and has already caused thousands of deaths. The analysis of death tolls helps to understand the dynamics of the conflict and to better allocate resources to the affected areas. In this article, we use information on the daily number of deaths to study temporal and spatial correlations in the data, and exploit this information to forecast events of deaths. We find that the number of deaths per day follows a log-normal distribution during the conflict. We have also identified strong correlations between cities and on consecutive days, implying that major deaths in one location are typically followed by major deaths in both the same location and in other areas. We find that war-related deaths are not random events and observing death tolls in some cities helps to better predict these numbers across the system., Comment: Comments and suggestions welcomed. 8 pages, 7 figures

Methicillin-resistant Staphylococcus aureus (MRSA) is a difficult-to-treat infection that only in the European Union affects about 150,000 patients and causes extra costs of 380 million Euros annually to the health-care systems. Increasing efforts have been taken to mitigate the epidemics and to avoid potential outbreaks in low endemic settings. Understanding the population dynamics of MRSA through modeling is essential to identify the causal mechanisms driving the epidemics and to generalize conclusions to different contexts. We develop an innovative high-resolution spatiotemporal contact network model of interactions between patients to reproduce the hospital population in the context of the Stockholm County in Sweden and simulate the spread of MRSA within this population. Our model captures the spatial and temporal heterogeneity caused by human behavior and by the dynamics of mobility within wards and hospitals. We estimate that in this population the epidemic threshold is at about 0.008. We also identify that these heterogeneous contact patterns cause the emergence of super-spreader patients and a polynomial growth of the epidemic curve. We finally study the effect of standard intervention control strategies and identify that screening is more effective than improved hygienic in order to cause smaller or null outbreaks.

Respondent-driven sampling (RDS) is a link-tracing sampling method that is especially suitable for sampling hidden populations. RDS combines an efficient snowball-type sampling scheme with inferential procedures that yield unbiased population estimates under some assumptions about the sampling procedure and population structure. Several seed individuals are typically used to initiate RDS recruitment. However, standard RDS estimation theory assume that all sampled individuals originate from only one seed. We present an estimator, based on a random walk with teleportation, which accounts for the multiple seed structure of RDS. The new estimator can also be used on populations with disconnected social networks. We numerically evaluate our estimator by simulations on artificial and real networks. Our estimator outperforms previous estimators, especially when the proportion of seeds in the sample is large. We recommend our new estimator to be used in RDS studies, in particular when the number of seeds is large or the social network of the population is disconnected.

The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing processes or spiking neurons, and epidemic and opinion formation processes on social networks. Empirically, the inter-event times of various phenomena obey long-tailed distributions. The Gillespie algorithm and its variants either assume Poisson processes (i.e., exponentially distributed inter-event times), use particular functions for time courses of the event rate, or work for non-Poissonian renewal processes, including the case of long-tailed distributions of inter-event times, but at a high computational cost. In the present study, we propose an innovative Gillespie algorithm for renewal processes on the basis of the Laplace transform. The algorithm makes use of the fact that a class of point processes is represented as a mixture of Poisson processes with different event rates. The method is applicable to multivariate renewal processes whose survival function of inter-event times is completely monotone. It is an exact algorithm and works faster than a recently proposed Gillespie algorithm for general renewal processes, which is exact only in the limit of infinitely many processes. We also propose a method to generate sequences of event times with a tunable amount of positive correlation between inter-event times. We demonstrate our algorithm with exact simulations of epidemic processes on networks, finding that a realistic amount of positive correlation in inter-event times only slightly affects the epidemic dynamics., Comment: 3 figures, 1 table

The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We develop an individual-based approximation for the susceptible-infected-recovered epidemic model applicable to arbitrary dynamic networks. Our framework provides, at the individual-level, the probability flow over time associated with the infection dynamics. This computationally efficient framework discards the correlation between the states of different nodes, yet provides accurate results in approximating direct numerical simulations. It naturally captures the temporal heterogeneities and correlations of contact sequences, fundamental ingredients regulating the timing and size of an epidemic outbreak. Using real-life data, we show that the static network model overestimates the reproduction number but underestimates the infection potential of super-spreading individuals. The high accuracy of our approximation further allows us to detect the index individual of an epidemic outbreak.

We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a homogeneous initial configuration, we show that temporal and structural heterogeneities, characteristic of real-world networks, spontaneously emerge. This theoretically tractable model thus contributes to the understanding of the dynamics of human activity and interaction networks.

Urbanization promotes economy, mobility, access and availability of resources, but on the other hand, generates higher levels of pollution, violence, crime, and mental distress. The health consequences of the agglomeration of people living close together are not fully understood. Particularly, it remains unclear how variations in the population size across cities impact the health of the population. We analyze the deviations from linearity of the scaling of several health-related quantities, such as the incidence and mortality of diseases, external causes of death, wellbeing, and health-care availability, in respect to the population size of cities in Brazil, Sweden and the USA. We find that deaths by non-communicable diseases tend to be relatively less common in larger cities, whereas the per-capita incidence of infectious diseases is relatively larger for increasing population size. Healthier life style and availability of medical support are disproportionally higher in larger cities. The results are connected with the optimization of human and physical resources, and with the non-linear effects of social networks in larger populations. An urban advantage in terms of health is not evident and using rates as indicators to compare cities with different population sizes may be insufficient., Comment: 12 pages

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the strong assumption that networks are static entities where temporal aspects can be neglected. Here we propose a generalised formalism for linear dynamics on complex networks, able to incorporate statistical properties of the timings at which events occur. We show that the diffusion dynamics is affected by the network community structure and by the temporal properties of waiting times between events. We identify the main mechanism --- network structure, burstiness or fat-tails of waiting times --- determining the relaxation times of stochastic processes on temporal networks, in the absence of temporal-structure correlations. We identify situations when fine-scale structure can be discarded from the description of the dynamics or, conversely, when a fully detailed model is required due to temporal heterogeneities., Comment: Fundamental revision from v1

If we can lower the number of people needed to vaccinate for a community to be immune against contagious diseases, we can save resources and life. A key to reach such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely to become infected and effective to spread the disease than the average. Fortunately, the very behavior that makes these people important to vaccinate can help us finding them. People you have met recently are more likely to be socially active and thus central in the contact pattern, and important to vaccinate. We propose two immunization schemes exploiting temporal contact patterns. Both of these rely only on obtainable, local information and could implemented in practice. We show that these schemes outperform benchmark protocols in four real data sets under various epidemic scenarios. The data sets are dynamic, which enables us to make more realistic evaluations than other studies - we use information only about the past to perform the vaccination and the future to simulate disease outbreaks. We also use models to elucidate the mechanisms behind how the temporal structures make our immunization protocols efficient.

Like many other social phenomena, prostitution is increasingly coordinated over the Internet. The online behavior affects the offline activity; the reverse is also true. We investigated the reported sexual contacts between 6,624 anonymous escorts and 10,106 sex-buyers extracted from an online community from its beginning and six years on. These sexual encounters were also graded and categorized (in terms of the type of sexual activities performed) by the buyers. From the temporal, bipartite network of posts, we found a full feedback loop in which high grades on previous posts affect the future commercial success of the sex-worker, and vice versa. We also found a peculiar growth pattern in which the turnover of community members and sex workers causes a sublinear preferential attachment. There is, moreover, a strong geographic influence on network structure-the network is geographically clustered but still close to connected, the contacts consistent with the inverse-square law observed in trading patterns. We also found that the number of sellers scales sublinearly with city size, so this type of prostitution does not, comparatively speaking, benefit much from an increasing concentration of people.

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling, after an introduction to the main concepts and models. A diversity of phenomena are surveyed, which may be classified into no less than 22 areas, providing a clear indication of the impact of the field of complex networks., Comment: 103 pages, 3 figures and 7 tables. A working manuscript, suggestions are welcomed