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.
Resilience denotes the capacity of a system to withstand shocks and its ability to recover from them. We develop a framework to quantify the resilience of highly volatile, non-equilibrium social organizations, such as collectives or collaborating teams. It consists of four steps: (i) \emph{delimitation}, i.e., narrowing down the target systems, (ii) \emph{conceptualization}, .e., identifying how to approach social organizations, (iii) formal \emph{representation} using a combination of agent-based and network models, (iv) \emph{operationalization}, i.e. specifying measures and demonstrating ho…
Recent years have seen the world become a closely connected society with the emergence of different types of social networks. Online social networks have provided a way to bridge long distances and establish numerous communication channels which were not possible earlier. These networks exhibit interesting behavior under intentional attacks and random failures where different structural properties influence the resilience in different ways. In this paper, we perform two sets of experiments and draw conclusions from the results pertaining to the resilience of social networks. The first experime…
Social networks of engagement sometimes dramatically collapse. A widely adopted paradigm to understand this catastrophe dynamics is the threshold model but previous work only considered the irreversible K-core pruning process and the resulting kinetic activity patterns. Here we study the network alliance problem as a simplified model of social engagement by equilibrium statistical mechanics. Our theory reveals that the surviving kinetic alliances are out-of-equilibrium and atypical configurations which may become highly vulnerable to single-node-triggered cascading failures as they relax towar…
One of the most important tasks of urban and hazard planning is to mitigate the damages and minimize the costs of the recovery process after catastrophic events. The rapidity and the efficiency of the recovery process are commonly referred to as resilience. Despite the problem of resilience quantification has received a lot of attention, a mathematical definition of the resilience of an urban community, which takes into account the social aspects of a urban environment, has not yet been identified. In this paper we provide and test a methodology for the assessment of urban resilience to catast…
The term 'resilience' is increasingly being used in social-technical-environmental systems sciences and particularly also in the Earth system sciences. However, the diversity of resilience concepts and a certain (sometimes intended) openness of proposed definitions can lead to misunderstandings and may impede their application to complex systems modelling. We propose a guideline that aims to ease communication as well as to support systematic development of research questions and models in the context of resilience. It can be applied independently of the modelling framework or underlying theor…
This paper develops a community resilience optimization method subject to power flow constraints in the Cyber-Physical-Social Systems in Power Engineering, which is solved using a multi-agent-based algorithm. The tool that makes the nexus between electricity generation on the physical side and the consumers and the critical loads on the social side is the power flow algorithm. Specifically, the levels of emotion, empathy, cooperation, and the physical health of the consumers, prosumers are modeled in the proposed community resilience optimization approach while accounting for the electric powe…
We study the problem of the emergence of cooperation in the spatial Prisoner's Dilemma. The pioneering work by Nowak and May showed that large initial populations of cooperators can survive and sustain cooperation in a square lattice with imitate-the-best evolutionary dynamics. We revisit this problem in a cost-benefit formulation suitable for a number of biological applications. We show that if a fixed-amount reward is established for cooperators to share, a single cooperator can invade a population of defectors and form structures that are resilient to re-invasion even if the reward mechanis…
Collectives form non-equilibrium social structures characterised by a volatile dynamics. Individuals join or leave. Social relations change quickly. Therefore, differently from engineered or ecological systems, a resilient reference state cannot be defined. We propose a novel resilience measure combining two dimensions: robustness and adaptivity. We demonstrate how they can be quantified using data from a software developer collective. Our analysis reveals a resilience life cycle, i.e., stages of increasing resilience are followed by stages of decreasing resilience. We explain the reasons for …
In complex systems like financial market, risk tolerance of individuals is crucial for system resilience.The single-security price limit, designed as risk tolerance to protect investors by avoiding sharp price fluctuation, is blamed for feeding market panic in times of crash.The relationship between the critical market confidence which stabilizes the whole system and the price limit is therefore an important aspect of system resilience. Using a simplified dynamic model on networks of investors and stocks, an unexpected linear association between price limit and critical market confidence is th…
Cities are complex systems comprised of socioeconomic systems relying on critical services delivered by multiple physical infrastructure networks. Due to interdependencies between social and physical systems, disruptions caused by natural hazards may cascade across systems, amplifying the impact of disasters. Despite the increasing threat posed by climate change and rapid urban growth, how to design interdependencies between social and physical systems to achieve resilient cities have been largely unexplored. Here, we study the socio-physical interdependencies in urban systems and their effect…
We empirically analyze five online communities: Friendster, Livejournal, Facebook, Orkut, Myspace, to identify causes for the decline of social networks. We define social resilience as the ability of a community to withstand changes. We do not argue about the cause of such changes, but concentrate on their impact. Changes may cause users to leave, which may trigger further leaves of others who lost connection to their friends. This may lead to cascades of users leaving. A social network is said to be resilient if the size of such cascades can be limited. To quantify resilience, we use the k-co…
We evaluate the robustness and adaptivity of social groups with heterogeneous agents that are characterized by their binary state, their ability to change this state, their status and their preferred relations to other agents. To define group structures, we operationalize the hexagrams of the \emph{I Ching}. The relations and properties of agents are used to quantify their influence according to the social impact theory. From these influence values we derive a weighted stability measure for triads involving three agents, which is based on the weighted balance theory. It allows to quantify the …
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…
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…
The concept of resilience embodies the quest towards the ability to sustain shocks, to suffer from these shocks as little as possible, for the shortest time possible, and to recover with the full functionalities that existed before the perturbation. We propose an operation definition of resilience, seeing it as a measure of stress that is complementary to the risk measures. Emphasis is put on the distinction between stressors (the forces acting on the system) and stress (the internal reaction of the system to the stressors). This allows us to elaborate a classification of stress measures and o…
We examine a model of network formation in single-layer and multiplex networks in which individuals have positive incentives for social ties, closed triangles, and spillover edges. In particular, we investigate the influence of shocks to the network in which the cost of social ties changes after an initial equilibrium. We highlight the emergence of structural entrenchment: the retention of structural features, such as closed triangles and spillover edges, which are formed under historically different conditions from those currently driving network evolution. This work has broad implications fo…
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…
The COVID19 pandemic has highlighted the lack of resilience in supply chains, as global networks fail from disruptions at single nodes and connections. Through an overview of the existing vaccine and pharmaceutical supply chain publications focusing on resilience, as well as recent papers reporting modeling of resilience in supply chains across multiple fields, we find that models for supply chain resilience are few and most of them are focused on individual dimensions of resilience rather than on comprehensive strategy necessary for scaling up vaccine production and distribution in emergency …
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…
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…
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…
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…
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.
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…
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 degre…
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…
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…
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）
The success of open source projects crucially depends on the voluntary contributions of a sufficiently large community of users. Apart from the mere size of the community, interesting questions arise when looking at the evolution of structural features of collaborations between community members. In this article, we discuss several network analytic proxies that can be used to quantify different aspects of the social organisation in social collaboration networks. We particularly focus on measures that can be related to the cohesiveness of the communities, the distribution of responsibilities an…
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…
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…
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…
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…
Knowledge of time-variant functionality of real-world physical, social, and engineered networks is critical to the understanding of the resilience of networks facing external perturbations. The majority of existing studies, however, focus only on the topological properties of networks for resilience assessment, which does not fully capture their dynamical resilience. In this study, we evaluate and quantify network resilience based both on the functionality states of links and on topology. We propose three independent measures---the failure scaling index (FSI), the weighted degree scaling index…
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…
Setting up the physical principles of resilience in a model of the Earth System
Faculdade de Ciências da Universidade do Porto（波尔图大学理学院）；Centro de Física das Universidades do Minho e do Porto（米尼奥大学和波尔图大学物理中心）；Stockholm Resilience Centre, University of Stockholm（斯德哥尔摩大学斯德哥尔摩韧性中心）
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…
Online social media allows individuals to cluster around common interests - including hate. We show that tight-knit social clusters interlink to form resilient 'global hate highways' that bridge independent social network platforms, countries, languages and ideologies, and can quickly self-repair and rewire. We provide a mathematical theory that reveals a hidden resilience in the global axis of hate; explains a likely ineffectiveness of current control methods; and offers improvements. Our results reveal new science for networks-of-networks driven by bipartite dynamics, and should apply more b…
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…
We study the evolutionary Prisoner's Dilemma on two social networks obtained from actual relational data. We find very different cooperation levels on each of them that can not be easily understood in terms of global statistical properties of both networks. We claim that the result can be understood at the mesoscopic scale, by studying the community structure of the networks. We explain the dependence of the cooperation level on the temptation parameter in terms of the internal structure of the communities and their interconnections. We then test our results on community-structured, specifical…
Human conflict, geopolitical crises, terrorist attacks, and natural disasters can turn large parts of energy distribution networks offline. Europe's current gas supply network is largely dependent on deliveries from Russia and North Africa, creating vulnerabililties to social and political instabilities. During crises, less delivery may mean greater congestion, as the pipeline network is used in ways it has not been designed for. Given the importance of the security of natural gas supply, we develop a model to handle network congestion on various geographical scales. We offer a resilient respo…
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 …
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…
