Emergence,Evolution and Scaling of Online Social Networks

Online social networks have become increasingly ubiquitous and understanding their structural, dynamical, and scaling properties not only is of fundamental interest but also has a broad range of applications. Such networks can be extremely dynamic, generated almost instantaneously by, for example, breaking-news items. We investigate a common class of online social networks, the user-user retweeting networks, by analyzing the empirical data collected from Sina Weibo (a massive twitter-like microblogging social network in China) with respect to the topic of the 2011 Japan earthquake. We uncover a number of algebraic scaling relations governing the growth and structure of the network and develop a probabilistic model that captures the basic dynamical features of the system. The model is capable of reproducing all the empirical results. Our analysis not only reveals the basic mechanisms underlying the dynamics of the retweeting networks, but also provides general insights into the control of information spreading on such networks.     

What's in a crowd? Analysis of face-to-face behavioral networks

The availability of new data sources on human mobility is opening new avenues for investigating the interplay of social networks, human mobility and dynamical processes such as epidemic spreading. Here we analyze data on the time-resolved face-to-face proximity of individuals in large-scale real-world scenarios. We compare two settings with very different properties, a scientific conference and a long-running museum exhibition. We track the behavioral networks of face-to-face proximity, and characterize them from both a static and a dynamic point of view, exposing differences and similarities. We use our data to investigate the dynamics of a susceptible-infected model for epidemic spreading that unfolds on the dynamical networks of human proximity. The spreading patterns are markedly different for the conference and the museum case, and they are strongly impacted by the causal structure of the network data. A deeper study of the spreading paths shows that the mere knowledge of static aggregated networks would lead to erroneous conclusions about the transmission paths on the dynamical networks.     

Detecting the Influence of Spreading in Social Networks with Excitable Sensor Networks

Detecting spreading outbreaks in social networks with sensors is of great significance in applications. Inspired by the formation mechanism of humans’ physical sensations to external stimuli, we propose a new method to detect the influence of spreading by constructing excitable sensor networks. Exploiting the amplifying effect of excitable sensor networks, our method can better detect small-scale spreading processes. At the same time, it can also distinguish large-scale diffusion instances due to the self-inhibition effect of excitable elements. Through simulations of diverse spreading dynamics on typical real-world social networks (Facebook, coauthor, and email social networks), we find that the excitable sensor networks are capable of detecting and ranking spreading processes in a much wider range of influence than other commonly used sensor placement methods, such as random, targeted, acquaintance and distance strategies. In addition, we validate the efficacy of our method with diffusion data from a real-world online social system, Twitter. We find that our method can detect more spreading topics in practice. Our approach provides a new direction in spreading detection and should be useful for designing effective detection methods.     

Finding Influential Spreaders from Human Activity beyond Network Location

Most centralities proposed for identifying influential spreaders on social networks to either spread a message or to stop an epidemic require the full topological information of the network on which spreading occurs. In practice, however, collecting all connections between agents in social networks can be hardly achieved. As a result, such metrics could be difficult to apply to real social networks. Consequently, a new approach for identifying influential people without the explicit network information is demanded in order to provide an efficient immunization or spreading strategy, in a practical sense. In this study, we seek a possible way for finding influential spreaders by using the social mechanisms of how social connections are formed in real networks. We find that a reliable immunization scheme can be achieved by asking people how they interact with each other. From these surveys we find that the probabilistic tendency to connect to a hub has the strongest predictive power for influential spreaders among tested social mechanisms. Our observation also suggests that people who connect different communities is more likely to be an influential spreader when a network has a strong modular structure. Our finding implies that not only the effect of network location but also the behavior of individuals is important to design optimal immunization or spreading schemes.     

Long-Term Evolution of Email Networks: Statistical Regularities,Predictability and Stability of Social Behaviors

In social networks, individuals constantly drop ties and replace them by new ones in a highly unpredictable fashion. This highly dynamical nature of social ties has important implications for processes such as the spread of information or of epidemics. Several studies have demonstrated the influence of a number of factors on the intricate microscopic process of tie replacement, but the macroscopic long-term effects of such changes remain largely unexplored. Here we investigate whether, despite the inherent randomness at the microscopic level, there are macroscopic statistical regularities in the long-term evolution of social networks. In particular, we analyze the email network of a large organization with over 1,000 individuals throughout four consecutive years. We find that, although the evolution of individual ties is highly unpredictable, the macro-evolution of social communication networks follows well-defined statistical patterns, characterized by exponentially decaying log-variations of the weight of social ties and of individuals’ social strength. At the same time, we find that individuals have social signatures and communication strategies that are remarkably stable over the scale of several years.     

Regimes and mechanisms of transient amplification in abstract and biological neural networks

Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes.     

Comparison of Contact Patterns Relevant for Transmission of Respiratory Pathogens in Thailand and the Netherlands Using Respondent-Driven Sampling

Understanding infection dynamics of respiratory diseases requires the identification and quantification of behavioural, social and environmental factors that permit the transmission of these infections between humans. Little empirical information is available about contact patterns within real-world social networks, let alone on differences in these contact networks between populations that differ considerably on a socio-cultural level. Here we compared contact network data that were collected in the Netherlands and Thailand using a similar online respondent-driven method. By asking participants to recruit contact persons we studied network links relevant for the transmission of respiratory infections. We studied correlations between recruiter and recruited contacts to investigate mixing patterns in the observed social network components. In both countries, mixing patterns were assortative by demographic variables and random by total numbers of contacts. However, in Thailand participants reported overall more contacts which resulted in higher effective contact rates. Our findings provide new insights on numbers of contacts and mixing patterns in two different populations. These data could be used to improve parameterisation of mathematical models used to design control strategies. Although the spread of infections through populations depends on more factors, found similarities suggest that spread may be similar in the Netherlands and Thailand.     

Entropy of dynamical social networks

Human dynamical social networks encode information and are highly adaptive. To characterize the information encoded in the fast dynamics of social interactions, here we introduce the entropy of dynamical social networks. By analysing a large dataset of phone-call interactions we show evidence that the dynamical social network has an entropy that depends on the time of the day in a typical week-day. Moreover we show evidence for adaptability of human social behavior showing data on duration of phone-call interactions that significantly deviates from the statistics of duration of face-to-face interactions. This adaptability of behavior corresponds to a different information content of the dynamics of social human interactions. We quantify this information by the use of the entropy of dynamical networks on realistic models of social interactions.     

Exploring the Complex Pattern of Information Spreading in Online Blog Communities

Information spreading in online social communities has attracted tremendous attention due to its utmost practical values in applications. Despite that several individual-level diffusion data have been investigated, we still lack the detailed understanding of the spreading pattern of information. Here, by comparing information flows and social links in a blog community, we find that the diffusion processes are induced by three different spreading mechanisms: social spreading, self-promotion and broadcast. Although numerous previous studies have employed epidemic spreading models to simulate information diffusion, we observe that such models fail to reproduce the realistic diffusion pattern. In respect to users behaviors, strikingly, we find that most users would stick to one specific diffusion mechanism. Moreover, our observations indicate that the social spreading is not only crucial for the structure of diffusion trees, but also capable of inducing more subsequent individuals to acquire the information. Our findings suggest new directions for modeling of information diffusion in social systems, and could inform design of efficient propagation strategies based on users behaviors.     

Civility vs. Incivility in Online Social Interactions: An Evolutionary Approach

Evidence is growing that forms of incivility–e.g. aggressive and disrespectful behaviors, harassment, hate speech and outrageous claims–are spreading in the population of social networking sites’ (SNS) users. Online social networks such as Facebook allow users to regularly interact with known and unknown others, who can behave either politely or rudely. This leads individuals not only to learn and adopt successful strategies for using the site, but also to condition their own behavior on that of others. Using a mean field approach, we define anevolutionary game framework to analyse the dynamics of civil and uncivil ways of interaction in online social networks and their consequences for collective welfare. Agents can choose to interact with others–politely or rudely–in SNS, or to opt out from online social networks to protect themselves from incivility. We find that, when the initial share of the population of polite users reaches a critical level, civility becomes generalized if its payoff increases more than that of incivility with the spreading of politeness in online interactions. Otherwise, the spreading of self-protective behaviors to cope with online incivility can lead the economyto non-socially optimal stationary states. JEL Codes: C61, C73, D85, O33, Z13. PsycINFO Codes: 2240, 2750.     

Community Size Effects on Epidemic Spreading in Multiplex Social Networks

The dynamical process of epidemic spreading has drawn much attention of the complex network community. In the network paradigm, diseases spread from one person to another through the social ties amongst the population. There are a variety of factors that govern the processes of disease spreading on the networks. A common but not negligible factor is people’s reaction to the outbreak of epidemics. Such reaction can be related information dissemination or self-protection. In this work, we explore the interactions between disease spreading and population response in terms of information diffusion and individuals’ alertness. We model the system by mapping multiplex networks into two-layer networks and incorporating individuals’ risk awareness, on the assumption that their response to the disease spreading depends on the size of the community they belong to. By comparing the final incidence of diseases in multiplex networks, we find that there is considerable mitigation of diseases spreading for full phase of spreading speed when individuals’ protection responses are introduced. Interestingly, the degree of community overlap between the two layers is found to be critical factor that affects the final incidence. We also analyze the consequences of the epidemic incidence in communities with different sizes and the impacts of community overlap between two layers. Specifically, as the diseases information makes individuals alert and take measures to prevent the diseases, the effective protection is more striking in small community. These phenomena can be explained by the multiplexity of the networked system and the competition between two spreading processes.     

Impact of the topology of global macroeconomic network on the spreading of economic crises

Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of a network of interacting macroeconomic agents. In this regard, from the perspective of collective network dynamics, here we explore how the topology of the global macroeconomic network affects the patterns of spreading of economic crises. Using a simple toy model of crisis spreading, we demonstrate that an individual country's role in crisis spreading is not only dependent on its gross macroeconomic capacities, but also on its local and global connectivity profile in the context of the world economic network. We find that on one hand clustering of weak links at the regional scale can significantly aggravate the spread of crises, but on the other hand the current network structure at the global scale harbors higher tolerance of extreme crises compared to more "globalized" random networks. These results suggest that there can be a potential hidden cost in the ongoing globalization movement towards establishing less-constrained, trans-regional economic links between countries, by increasing vulnerability of the global economic system to extreme crises.     

Evolution of Cooperation on Stochastic Dynamical Networks

Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are), the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure.     

Emergence of Blind Areas in Information Spreading

Recently, contagion-based (disease, information, etc.) spreading on social networks has been extensively studied. In this paper, other than traditional full interaction, we propose a partial interaction based spreading model, considering that the informed individuals would transmit information to only a certain fraction of their neighbors due to the transmission ability in real-world social networks. Simulation results on three representative networks (BA, ER, WS) indicate that the spreading efficiency is highly correlated with the network heterogeneity. In addition, a special phenomenon, namely Information Blind Areas where the network is separated by several information-unreachable clusters, will emerge from the spreading process. Furthermore, we also find that the size distribution of such information blind areas obeys power-law-like distribution, which has very similar exponent with that of site percolation. Detailed analyses show that the critical value is decreasing along with the network heterogeneity for the spreading process, which is complete the contrary to that of random selection. Moreover, the critical value in the latter process is also larger than that of the former for the same network. Those findings might shed some lights in in-depth understanding the effect of network properties on information spreading.     

From network structure to network reorganization: implications for adult neurogenesis

Networks can be dynamical systems that undergo functional and structural reorganization. One example of such a process is adult hippocampal neurogenesis, in which new cells are continuously born and incorporate into the existing network of the dentate gyrus region of the hippocampus. Many of these introduced cells mature and become indistinguishable from established neurons, joining the existing network. Activity in the network environment is known to promote birth, survival and incorporation of new cells. However, after epileptogenic injury, changes to the connectivity structure around the neurogenic niche are known to correlate with aberrant neurogenesis. The possible role of network-level changes in the development of epilepsy is not well understood. In this paper, we use a computational model to investigate how the structural and functional outcomes of network reorganization, driven by addition of new cells during neurogenesis, depend on the original network structure. We find that there is a stable network topology that allows the network to incorporate new neurons in a manner that enhances activity of the persistently active region, but maintains global network properties. In networks having other connectivity structures, new cells can greatly alter the distribution of firing activity and destroy the initial activity patterns. We thus find that new cells are able to provide focused enhancement of network only for small-world networks with sufficient inhibition. Network-level deviations from this topology, such as those caused by epileptogenic injury, can set the network down a path that develops toward pathological dynamics and aberrant structural integration of new cells.     

Does the sociality of pollinators shape the organisation of pollination networks?

A striking structural pattern of pollination networks is the presence of a few highly connected species which has implications for ecological and evolutionary processes that create and maintain diversity. To understand the structure and dynamics of pollination networks we need to know which mechanisms allow the emergence of highly connected species. We investigate whether social pollinator species are highly connected in pollination networks, and whether network structure is affected by the presence of high proportions of social pollinator species. Social insects are abundant, with long activity periods and, at the highest level of social organisation, specialised foraging castes. These three attributes are likely to increase the number of interactions of social species and, consequently, their role in pollination networks. We find that social species have, on average, more prominent network roles than solitary species, a possible mechanism being the individual‐rich colonies of social insects. However, when accounting for the shared evolutionary history of pollinators, sociality is only associated with highly interactive roles in Apidae. For apid bees, our structural equation analysis shows that the effect of sociality on species network roles is an indirect result of their high levels of interaction frequency. Despite the relative importance of sociality at a species‐level, an increasing proportion of social species in pollination networks did not affect overall network structure. Our results suggest that behavioural traits may shape patterns of interaction of individual species but not the network‐level organisation of species interactions. Instead, network structure appears to be determined by more general aspects of ecological systems such as interaction intimacy, patterns of niche overlap, and species abundance distributions.     

Bursty Communication Patterns Facilitate Spreading in a Threshold-Based Epidemic Dynamics

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.     

Emergence of Slow-Switching Assemblies in Structured Neuronal Networks

Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network connectivity underpin the propensity of neural networks to generate slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased firing within assemblies of neurons which transition slowly between different assemblies throughout the network. We show that the emergence of SSA activity is linked to spectral properties of the asymmetric synaptic weight matrix. In particular, the leading eigenvalues that dictate the slow dynamics exhibit a gap with respect to the bulk of the spectrum, and the associated Schur vectors exhibit a measure of block-localization on groups of neurons, thus resulting in coherent dynamical activity on those groups. Through simple rate models, we gain analytical understanding of the origin and importance of the spectral gap, and use these insights to develop new network topologies with alternative connectivity paradigms which also display SSA activity. Specifically, SSA dynamics involving excitatory and inhibitory neurons can be achieved by modifying the connectivity patterns between both types of neurons. We also show that SSA activity can occur at multiple timescales reflecting a hierarchy in the connectivity, and demonstrate the emergence of SSA in small-world like networks. Our work provides a step towards understanding how network structure (uncovered through advancements in neuroanatomy and connectomics) can impact on spatio-temporal neural activity and constrain the resulting dynamics.     

Modelling the control of interceptive actions

In recent years, several phenomenological dynamical models have been formulated that describe how perceptual variables are incorporated in the control of motor variables. We call these short-route models as they do not address how perception-action patterns might be constrained by the dynamical properties of the sensory, neural and musculoskeletal subsystems of the human action system. As an alternative, we advocate a long-route modelling approach in which the dynamics of these subsystems are explicitly addressed and integrated to reproduce interceptive actions. The approach is exemplified through a discussion of a recently developed model for interceptive actions consisting of a neural network architecture for the online generation of motor outflow commands, based on time-to-contact information and information about the relative positions and velocities of hand and ball. This network is shown to be consistent with both behavioural and neurophysiological data. Finally, some problems are discussed with regard to the question of how the motor outflow commands (i.e. the intended movement) might be modulated in view of the musculoskeletal dynamics.     

Active colonization dynamics and diversity patterns are influenced by dendritic network connectivity and species interactions

Habitat network connectivity influences colonization dynamics, species invasions, and biodiversity patterns. Recent theoretical work suggests dendritic networks, such as those found in rivers, alter expectations regarding colonization and dispersal dynamics compared with other network types. As many native and non‐native species are spreading along river networks, this may have important ecological implications. However, experimental studies testing the effects of network structure on colonization and diversity patterns are scarce. Up to now, experimental studies have only considered networks where sites are connected with small corridors, or dispersal was experimentally controlled, which eliminates possible effects of species interactions on colonization dynamics. Here, we tested the effect of network connectivity and species interactions on colonization dynamics using continuous linear and dendritic (i.e., river‐like) networks, which allow for active dispersal. We used a set of six protist species and one rotifer species in linear and dendritic microcosm networks. At the start of the experiment, we introduced species, either singularly or as a community within the networks. Species subsequently actively colonized the networks. We periodically measured densities of species throughout the networks over 2 weeks to track community dynamics, colonization, and diversity patterns. We found that colonization of dendritic networks was faster compared with colonization of linear networks, which resulted in higher local mean species richness in dendritic networks. Initially, community similarity was also greater in dendritic networks compared with linear networks, but this effect vanished over time. The presence of species interactions increased community evenness over time, compared with extrapolations from single‐species setups. Our experimental findings confirm previous theoretical work and show that network connectivity, species‐specific dispersal ability, and species interactions greatly influence the dispersal and colonization of dendritic networks. We argue that these factors need to be considered in empirical studies, where effects of network connectivity on colonization patterns have been largely underestimated.