Models of interacting social agents often represent agents as very simple entities having a small number of degrees of freedom, as exemplified by binary opinion models for instance. Understanding how such simple individual characteristics may emerge from potentially much more complex agents is thus a natural question. It has been proposed recently in [E. Bertin, P. Jensen, C.R. Phys. 20, 329 (2019)] that some types of interactions among agents with many internal degrees of freedom may lead to a `simplification' of agents, which are then effectively described by a small number of internal degrees of freedom. Here, we generalize the model to account for agents intrinsic heterogeneity. We find two different simplification regimes, one dominated by interactions, where agents become simple and identical as in the homogeneous model, and one where agents remain strongly heterogeneous although effectively having simple characteristics.
By means of extensive computer simulations, the authors consider the entangled coevolution of actions and social structure in a new version of a spatial Prisoner's Dilemma model that naturally gives way to a process of social differentiation. Diverse social roles emerge from the dynamics of the system: leaders are individuals getting a large payoff who are imitated by a considerable fraction of the population, conformists are unsatisfied cooperative agents that keep cooperating, and exploiters are defectors with a payoff larger than the average one obtained by cooperators. The dynamics generat…
Models of cooperation grounded on social networks and on the ability of individuals to choose actions and partners aim to describe human social behavior. Extensive computer simulations of these models give important insight in the social mechanisms behind emerging collective behavior. We consider the entangled co-evolution of actions and social structure in a new version of a spatial Prisoner's Dilemma model that naturally gives way to a process of social differentiation. Diverse social roles emerge from the dynamics of the system: leaders -individuals getting a large payoff who are imitated b…
Assessing quantitatively the state and dynamics of a social system is a very difficult problem. It is of great importance for both practical and theoretical reasons such as establishing the efficiency of social action programs, detecting possible community needs or allocating resources. In this paper we propose a new general theoretical framework for the study of social complexity, based on the relation of complexity and entropy in combination with evolutionary dynamics to asses the dynamics of the system. Imposing the second law of thermodynamics, we study the conditions under which cooperati…
Research institutions provide the infrastructure for scientific discovery, yet their role in the production of knowledge is not well characterized. To address this gap, we analyze interactions of researchers within and between institutions from millions of scientific papers. Our analysis reveals that the number of collaborations scales superlinearly with institution size, though at different rates (heterogeneous densification). We also find that the number of institutions scales with the number of researchers as a power law (Heaps' law) and institution sizes approximate Zipf's law. These patte…
The emergence due to the outbreak of the COVID-19 disease, caused by the SARS-CoV-2 virus, suddenly erupted at the beginning of 2020 in China and soon spread worldwide. This has caused an outstanding increase on research about the virus itself and, more in general, epidemics in many scientific fields. In this work we focus on the dynamics of the epidemic spreading and how it can be affected by the individual variability in compliance with social norms, i.e., in the adoption of health and hygienic social norms by population's members.
We introduce and study a general model of social network formation and evolution based on the concept of preferential link formation between similar nodes and increased similarity between connected nodes. The model is studied numerically and analytically for three definitions of similarity. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence. We suggest that the positive feedback between linking and similarity which is responsible for the model's behaviour is also an important mechanism in real social networks.
The interactions among human beings represent the backbone of our societies. How people interact, establish new connections, and allocate their activities among these links can reveal a lot of our social organization. Despite focused attention by very diverse scientific communities, we still lack a first-principles modeling framework able to account for the birth and evolution of social networks. Here, we tackle this problem by looking at social interactions as a way to explore a very peculiar space, namely the adjacent possible space, i.e., the set of individuals we can meet at any given poin…
Social influence drives both offline and online human behaviour. It pervades cultural markets, and manifests itself in the adoption of scientific and technical innovations as well as the spread of social practices. Prior empirical work on the diffusion of innovations in spatial regions or social networks has largely focused on the spread of one particular technology among a subset of all potential adopters. It has also been difficult to determine whether the observed collective behaviour is driven by natural influence processes, or whether it follows external signals such as media or marketing…
The focus of structural balance theory is dedicated to social benefits, while in a real network individual benefits sometimes get the importance as well. In Strauss's model, the local minima are modeled by considering an individual term besides a social one and the assumption is based on equal strength of individual benefits. The results show that the competition between two terms leads to a phase transition between individual and social benefits and there is a critical point, $CP$, that represents a first-order phase transition in the network. Concerning a real network of relations, individua…
How self-organization leads to the emergence of structure in social populations remains a fascinating and open question in the study of complex systems. One frequently observed structure that emerges again and again across systems is that of self-similar community, i.e., homophily. We use a game theoretic perspective to explore a case in which individuals choose affiliation partnerships based on only two factors: the value they place on having social contacts, and their risk tolerance for exposure to threat derived from social contact (e.g., infectious disease, threatening ideas, etc.). We sho…
The study of the organization of social networks is important for understanding of opinion formation, rumor spreading, and the emergence of trends and fashion. This paper reports empirical analysis of networks extracted from four leading sites with social functionality (Delicious, Flickr, Twitter and YouTube) and shows that they all display a scale-free leadership structure. To reproduce this feature, we propose an adaptive network model driven by social recommending. Artificial agent-based simulations of this model highlight a "good get richer" mechanism where users with broad interests and g…
Despite global connectivity, societies seem to be increasingly polarized and fragmented. This phenomenon is rooted in the underlying complex structure and dynamics of social systems. Far from homogeneously mixing or adopting conforming views, individuals self-organize into groups at multiple scales, ranging from families up to cities and cultures. In this paper, we study the fragmented structure of the American society using mobility and communication networks obtained from geo-located social media data. We find self-organized patches with clear geographical borders that are consistent between…
Power law degree distribution was shown in many complex networks. However, in most real systems, deviation from power-law behavior is observed in social and economical networks and emergence of giant hubs is obvious in real network structures far from the tail of power law. We propose a model based on the information transparency (transparency means how much the information is obvious to others). This model can explain power structure in societies with non-transparency in information delivery. The emergence of ultra powerful nodes is explained as a direct result of censorship. Based on these a…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (=degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents gamma ~ 1 than have been assum…
Polarization is a ubiquitous phenomenon in social systems. Empirical studies document substantial evidence for opinion polarization across social media, showing a typical bipolarized pattern devising individuals into two groups with opposite opinions. While coevolving network models have been proposed to understand polarization, existing works cannot generate a stable bipolarized structure. Moreover, a quantitative and comprehensive theoretical framework capturing generic mechanisms governing polarization remains unaddressed. In this paper, we discover a universal scaling law for opinion distr…
We study a networked version of the minority game in which agents can choose to follow the choices made by a neighbouring agent in a social network. We show that for a wide variety of networks a leadership structure always emerges, with most agents following the choice made by a few agents. We find a suitable parameterisation which highlights the universal aspects of the behaviour and which also indicates where results depend on the type of social network.
We investigate the impact of an exogenous environment on the emergence of social herding of economic sentiment. An interactions-driven dynamics of economic sentiment is modeled by an Ising model on a large (two-dimensional) square lattice. The individual states are called optimism and pessimism. The exogenous environment is modeled as a sequence of random events, which might have a positive or negative influence on economic sentiment. These exogenous events can be frequent or rare, have a lasting impact or a non-lasting impact. Impact of events is inhomogeneous over the lattice, as individuals…
Rumor models consider that information transmission occurs with the same probability between each pair of nodes. However, this assumption is not observed in social networks, which contain influential spreaders. To overcome this limitation, we assume that central individuals have a higher capacity of convincing their neighbors than peripheral subjects. By extensive numerical simulations we find that the spreading is improved in scale-free networks when the transmission probability is proportional to PageRank, degree, and betweenness centrality. In addition, the results suggest that the spreadin…
People usually get involved in multiple social networks to enjoy new services or to fulfill their needs. Many new social networks try to attract users of other existing networks to increase the number of their users. Once a user (called source user) of a social network (called source network) joins a new social network (called target network), a new inter-network link (called anchor link) is formed between the source and target networks. In this paper, we concentrated on predicting the formation of such anchor links between heterogeneous social networks. Unlike conventional link prediction pro…
We here present a fixed agents version of an original model of the emergence of hierarchies among social agents first introduced by Bonabeau \textit{et al}. Having interactions occurring on a social network rather than among 'walkers' doesn't drastically alter the dynamics. But it makes social structures more stable and give a clearer picture of the social organisation in a `mixed' regime.
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $R_0$ which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an a…
Social relationships characterize the interactions that occur within social species and may have an important impact on collective animal motion. Here, we consider a variation of the standard Vicsek model for collective motion in which interactions are mediated by an empirically motivated scale-free topology that represents a heterogeneous pattern of social contacts. We observe that the degree of order of the model is strongly affected by network heterogeneity: more heterogeneous networks show a more resilient ordered state; while less heterogeneity leads to a more fragile ordered state that c…
We argue that when a social convergence mechanism exists and is strong enough, one should expect the emergence of a well defined "field", i.e. a slowly evolving, local quantity around which individual attributes fluctuate in a finite range. This condensation phenomenon is well illustrated by the Deffuant-Weisbuch opinion model for which we provide a natural extension to allow for spatial heterogeneities. We show analytically and numerically that the resulting dynamics of the emergent field is a noisy diffusion equation that has a slow dynamics. This random diffusion equation reproduces the lon…
Heterogeneous adoption thresholds exist widely in social contagions, but were always neglected in previous studies. We first propose a non-Markovian spreading threshold model with general adoption threshold distribution. In order to understand the effects of heterogeneous adoption thresholds quantitatively, an edge-based compartmental theory is developed for the proposed model. We use a binary spreading threshold model as a specific example, in which some individuals have a low adoption threshold (i.e., activists) while the remaining ones hold a relatively high adoption threshold (i.e., bigots…
Social Influence and Unfollowing Accelerate the Emergence of Echo Chambers
Graduate School of Informatics, Nagoya University（名古屋大学情报学研究科）；JST, PRESTO（日本科学技术振兴机构，PRESTO项目）；Center for Complex Networks and Systems Research, Indiana University Bloomington（印第安纳大学布卢明顿分校复杂网络与系统研究中心）；Luddy School of Informatics, Computing, and Engineering, Indiana University（印第安纳大学卢迪信息、计算与工程学院）；School of Information, University of Michigan（密歇根大学信息学院）；Network Science Institute, Indiana University（印第安纳大学网络科学研究所）；Department of Computer Science and Engineering, University of South Florida（南佛罗里达大学计算机科学与工程系）
Modern political interaction is characterized by strong partisanship and a lack of interest in information sharing and agreement across party lines. It remains largely unclear how such partisan echo chambers arise and how they coevolve with opinion formation. Here we explore the emergence of these structures through the lens of coevolutionary games. In our model, the payoff of an individual is determined jointly by the magnitude of their opinion, their degree of conformity with their social neighbors, and the benefit of having social connections. Each individual can simultaneously adjust their…
We examine a weighted-network multi-agent model with preferential selection such that agents choose partners with the probability $p(w)$, where $w$ is the number of their past selections. When $p(w)$ increases sublinearly with the number of past selections ($p(w)\sim w^α, \ α<1$), agents develop a uniform preference for all other agents. At $α=1$, this state looses stability and more complex structures form. For a superlinear increase ($α>1$), strong heterogeneities emerge and agents make selections mainly within small and sometimes asymmetric clusters. Even in a few-agent case, formation of s…
Human behavior often exhibit a scheme in which individuals adopt indifferent, neutral, or radical positions on a given topic. The mechanisms leading to community formation are strongly related with social pressure and the topology of the contact network. Here, we discuss an approach to model social behavior which accounts for the protection by alike peers proportional to their relative abundance in the closest neighborhood. We explore the ensuing non-linear dynamics emphasizing the role of the specific structure of the social network, modeled by scale-free graphs. We find that both coexistence…
Social network alignment has been an important research problem for social network analysis in recent years. With the identified shared users across networks, it will provide researchers with the opportunity to achieve a more comprehensive understanding of users' social activities both within and across networks. Social network alignment is a very difficult problem. Besides the challenges introduced by the network heterogeneity, the network alignment problem can be reduced to a combinatorial optimization problem with an extremely large search space. The learning effectiveness and efficiency of…
We propose a stochastic model for the diffusion of topics entering a social network modeled by a Watts-Strogatz graph. Our model sets into play an implicit competition between these topics as they vie for the attention of users in the network. The dynamics of our model are based on notions taken from real-world OSNs like Twitter where users either adopt an exogenous topic or copy topics from their neighbors leading to endogenous propagation. When instantiated correctly, the model achieves a viral regime where a few topics garner unusually good response from the network, closely mimicking the b…
Far beyond its relevance for commercial and political marketings, opinion formation and decision making processes are central for representative democracy, government functioning, and state organization. In the present report, a stochastic agent-based model is investigated. The model assumes that bounded confidence and homophily mechanisms drive both opinion dynamics and social network evolution through either rewiring or breakage of social contacts. In addition to the classical transition from global consensus to opinion polarization, our main findings are (i) a cascade of fragmentation of th…
We propose a model for social dynamics on a network. In this model each actor holds a position on some issue, actors and their opinions being associated to vertices of the graph, and, additionally, the actors hold opinions of one another, with these opinions being associated to edges in the graph. These quantities are allowed to evolve according to the gradient flow of a natural free energy. We show that for a small spread in opinions the model converges to a consensus state, where all actors hold the same position. For a larger spread in opinion there is a phase transition marked by the birth…
Multi-agent models often describe populations segregated either in the physical space, i.e. subdivided in metapopulations, or in the ecology of opinions, i.e. partitioned in echo chambers. Here we show how the interplay between homophily and social influence controls the emergence of both kinds of segregation in a simple model of mobile agents, endowed with a continuous opinion variable. In the model, physical proximity determines a progressive convergence of opinions but differing opinions result in agents moving away from each others. This feedback between mobility and social dynamics determ…
LARODEC, University of Tunis（突尼斯大学LARODEC实验室）；IRISA, University of Rennes 1（雷恩第一大学IRISA研究所）
Nowadays, social networks such as Twitter, Facebook and LinkedIn become increasingly popular. In fact, they introduced new habits, new ways of communication and they collect every day several information that have different sources. Most existing research works fo-cus on the analysis of homogeneous social networks, i.e. we have a single type of node and link in the network. However, in the real world, social networks offer several types of nodes and links. Hence, with a view to preserve as much information as possible, it is important to consider so-cial networks as heterogeneous and uncertain…
The emergence of politically driven divisions in online discussion networks has attracted a wealth of literature, but also one which has thus far been largely limited to single country studies. Hence whilst there is good evidence that these networks do divide and fragment into what are often described as "echo chambers", we know little about the factors which might explain this division or make networks more or less fragmented, as studies have been limited to a small number of political groupings with limited possibilities for systematic comparison. This paper seeks to remedy this deficit, by …
We have two main aims in this paper. First we use theories of disease spreading on networks to look at the COVID-19 epidemic on the basis of individual contacts -- these give rise to predictions which are often rather different from the homogeneous mixing approaches usually used. Our second aim is to look at the role of social deprivation, again using networks as our basis, in the spread of this epidemic. We choose the city of Kolkata as a case study, but assert that the insights so obtained are applicable to a wide variety of urban environments which are densely populated and where social ine…
We study variants of the SEIR model for interpreting some qualitative features of the statistics of the Covid-19 epidemic in France. Standard SEIR models distinguish essentially two regimes: either the disease is controlled and the number of infected people rapidly decreases, or the disease spreads and contaminates a significant fraction of the population until herd immunity is achieved. After lockdown, at first sight it seems that social distancing is not enough to control the outbreak. We discuss here a possible explanation, namely that the lockdown is creating social heterogeneity: even if …
Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive peak slightly past the average degree. The way traditional models imprint assortativity on top of pre-defined topologies is via degree-preserving link permutations, which however destroy the particular graph's hierarchical traits of clustering. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties a…
How do shared conventions emerge in complex decentralized social systems? This question engages fields as diverse as linguistics, sociology and cognitive science. Previous empirical attempts to solve this puzzle all presuppose that formal or informal institutions, such as incentives for global agreement, coordinated leadership, or aggregated information about the population, are needed to facilitate a solution. Evolutionary theories of social conventions, by contrast, hypothesize that such institutions are not necessary in order for social conventions to form. However, empirical tests of this …
The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes' thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation.…
Node copying is an important mechanism for network formation, yet most models assume uniform copying rules. Motivated by observations of heterogeneous triadic closure in real networks, we introduce the concept of a hidden network model - a generative two-layer model in which an observed network evolves according to the structure of an underlying hidden layer - and apply the framework to a model of heterogeneous copying. Framed in a social context, these two layers represent a node's inner social circle, and wider social circle, such that the model can bias copying probabilities towards, or aga…
Online social dynamics based on human endeavours exhibit prominent complexity in the emergence of new features embodied in the appearance of collective social values. The vast amount of empirical data collected at various websites provides a unique opportunity to quantitative study od the underlying social dynamics in full analogy with complex systems in the physics laboratory. Here, we briefly describe the extent of these analogies and indicate the methods from other science disciplines that the physics theory can incorporate to provide the adequate description of human entities and principle…
Network autocorrelation models are widely used to evaluate the impact of social influence on some variable of interest. This is a large class of models that parsimoniously accounts for how one's neighbors influence one's own behaviors or opinions by incorporating the network adjacency matrix into the joint distribution of the data. These models assume homogeneous susceptibility to social influence, however, which may be a strong assumption in many contexts. This paper proposes a hierarchical model that allows the influence parameter to be a function of individual attributes and/or of local net…
Within the context of social balance theory, much attention has been paid to the attainment and stability of unipolar or bipolar societies. However, multipolar societies are commonplace in the real world, despite the fact that the mechanism of their emergence is much less explored. Here, we investigate the evolution of a society of interacting agents with friendly (positive) and enmity (negative) relations into a final stable multipolar state. Triads are assigned energy according to the degree of tension they impose on the network. Agents update their connections in order to decrease the total…
There is a tragedy of the traffic analogous to the tragedy of the commons that can be caused by overtaking. We analyze the effect of overtaking in a minimal model of vehicular traffic, the model proposed by Nagel and Schreckenberg, with two types of drivers: drivers that overtake and drivers that do not. We show that, under certain circumstances, overtaking is good because it increases the road capacity and minimizes the mean time spent by the driver on the road. However, when these conditions are not met, overtaking is harmful to all. More specifically, we found that a social dilemma emerges …
Observable social traits determine how we interact in society and remain pervasive even in our globalized world. While a popular hypothesis states that they may help promote cooperation, the alternative explanation that they facilitate coordination has gained ground in recent years. Here we explore this framework and present a model that investigates the role of ethnic markers in coordination games. We consider fixed markers characterizing agents that use reinforcement learning to update their strategies in the game. For a wide range of parameters, we observe the emergence of a collective equi…
The origin of population-scale coordination has puzzled philosophers and scientists for centuries. Recently, game theory, evolutionary approaches and complex systems science have provided quantitative insights on the mechanisms of social consensus. However, the literature is vast and widely scattered across fields, making it hard for the single researcher to navigate it. This short review aims to provide a compact overview of the main dimensions over which the debate has unfolded and to discuss some representative examples. It focuses on those situations in which consensus emerges 'spontaneous…
Motivated by online social networks that are linked together through overlapping users, we study the influence maximization problem on a multiplex, with each layer endowed with its own model of influence diffusion. This problem is a novel version of the influence maximization problem that necessitates new analysis incorporating the type of propagation on each layer of the multiplex. We identify a new property, generalized deterministic submodular, which when satisfied by the propagation in each layer, ensures that the propagation on the multiplex overall is submodular -- for this case, we form…
Online social networks have gained great success in recent years and many of them involve multiple kinds of nodes and complex relationships. Among these relationships, social links among users are of great importance. Many existing link prediction methods focus on predicting social links that will appear in the future among all users based upon a snapshot of the social network. In real-world social networks, many new users are joining in the service every day. Predicting links for new users are more important. Different from conventional link prediction problems, link prediction for new users …
Real social interactions occur on networks in which each individual is connected to some, but not all, of others. In social dilemma games with a fixed population size, heterogeneity in the number of contacts per player is known to promote evolution of cooperation. Under a common assumption of positively biased payoff structure, well-connected players earn much by playing frequently, and cooperation once adopted by well-connected players is unbeatable and spreads to others. However, maintaining a social contact can be costly, which would prevent local payoffs from being positively biased. In re…
