PageRank model of opinion formation on Ulam networks

We consider a PageRank model of opinion formation on Ulam networks, generated by the intermittency map and the typical Chirikov map. The Ulam networks generated by these maps have certain similarities with such scale-free networks as the World Wide Web (WWW), showing an algebraic decay of the PageRank probability. We find that the opinion formation process on Ulam networks has certain similarities but also distinct features comparing to the WWW. We attribute these distinctions to internal differences in network structure of the Ulam and WWW networks. We also analyze the process of opinion formation in the frame of generalized Sznajd model which protects opinion of small communities.     

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.     

Discrete Opinion Dynamics on Online Social Networks

This paper focuses on the dynamics of binary opinions {+1,-1} on online social networks consisting of heterogeneous actors.In our model,actors update their opinions under the interplay of social influence and selfaffirmation,which leads to rich dynamical behaviors on online social networks.We find that the opinion leading to the consensus features an advantage of the initially weighted fraction based on actors' strength over the other,instead of the population.For the role of specific actors,the consensus converges towards the opinion that a small fraction of high-strength actors hold,and individual diversity of self-affirmation slows down the ordering process of consensus.These indicate that high-strength actors play an essential role in opinion formation with strong social influence as well as high persistence.Further investigations show that the initial fraction of high-strength actors to dominate the evolution depends on the heterogeneity of the strength distribution,and less high-strength actors are needed in the case of a smaller exponent of power-law distribution of actors' strength.Our study provides deep insights into the role of social influence and self-affirmation on opinion formation on online social networks.     

Renormalizing Sznajd model on complex networks taking into account the effects of growth mechanisms

We present a renormalization approach to solve the Sznajd opinion formation model on complex networks. For the case of two opinions, we present an expression of the probability of reaching consensus for a given opinion as a function of the initial fraction of agents with that opinion. The calculations reproduce the sharp transition of the model on a fixed network, as well as the recently observed smooth function for the model when simulated on a growing complex networks.     

Convergence to global consensus in opinion dynamics under a nonlinear voter model

We propose a nonlinear voter model to study the emergence of global consensus in opinion dynamics. In our model, agent i agrees with one of binary opinions with the probability that is a power function of the number of agents holding this opinion among agent i and its nearest neighbors, where an adjustable parameter α controls the effect of herd behavior on consensus. We find that there exists an optimal value of α leading to the fastest consensus for lattices, random graphs, small-world networks and scale-free networks. Qualitative insights are obtained by examining the spatiotemporal evolution of the opinion clusters.     

Non-consensus Opinion Models on Complex Networks

Social dynamic opinion models have been widely studied to understand how interactions among individuals cause opinions to evolve. Most opinion models that utilize spin interaction models usually produce a consensus steady state in which only one opinion exists. Because in reality different opinions usually coexist, we focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao et al. (Phys. Rev. Lett. 103:01870, 2009). The NCO model in random networks displays a second order phase transition that belongs to regular mean field percolation and is characterized by the appearance (above a certain threshold) of a large spanning cluster of the minority opinion. We generalize the NCO model by adding a weight factor W to each individual’s original opinion when determining their future opinion (NCOW model). We find that as W increases the minority opinion holders tend to form stable clusters with a smaller initial minority fraction than in the NCO model. We also revisit another non-consensus opinion model based on the NCO model, the inflexible contrarian opinion (ICO) model (Li et al. in Phys. Rev. E 84:066101, 2011), which introduces inflexible contrarians to model the competition between two opinions in a steady state. Inflexible contrarians are individuals that never change their original opinion but may influence the opinions of others. To place the inflexible contrarians in the ICO model we use two different strategies, random placement and one in which high-degree nodes are targeted. The inflexible contrarians effectively decrease the size of the largest rival-opinion cluster in both strategies, but the effect is more pronounced under the targeted method. All of the above models have previously been explored in terms of a single network, but human communities are usually interconnected, not isolated. Because opinions propagate not only within single networks but also between networks, and because the rules of opinion formation within a network may differ from those between networks, we study here the opinion dynamics in coupled networks. Each network represents a social group or community and the interdependent links joining individuals from different networks may be social ties that are unusually strong, e.g., married couples. We apply the non-consensus opinion (NCO) rule on each individual network and the global majority rule on interdependent pairs such that two interdependent agents with different opinions will, due to the influence of mass media, follow the majority opinion of the entire population. The opinion interactions within each network and the interdependent links across networks interlace periodically until a steady state is reached. We find that the interdependent links effectively force the system from a second order phase transition, which is characteristic of the NCO model on a single network, to a hybrid phase transition, i.e., a mix of second-order and abrupt jump-like transitions that ultimately becomes, as we increase the percentage of interdependent agents, a pure abrupt transition. We conclude that for the NCO model on coupled networks, interactions through interdependent links could push the non-consensus opinion model to a consensus opinion model, which mimics the reality that increased mass communication causes people to hold opinions that are increasingly similar. We also find that the effect of interdependent links is more pronounced in interdependent scale free networks than in interdependent Erd?s Rényi networks.     

Social bots and mass media manipulated public opinion through dual opinion climate

Opinion dynamics models based on the multi-agent method commonly assume that interactions between individuals in a social network result in changes in their opinions.However,formation of public opinion in a social network is a macroscopic statistical result of opinions of all expressive individuals(corresponding to silent individuals).Therefore,public opinion can be manipulated not only by changing individuals'opinions,but also by changing their states of expression(or silence)which can be interpreted as the phenomenon"spiral of silence"in social psychology.Based on this theory,we establish a"dual opinion climate"model,involving social bots and mass media through a multi-agent method,to describe mechanism for manipulation of public opinion in social networks.We find that both social bots(as local variables)and mass media(as a global variable)can interfere with the formation of public opinion,cause a significant superposition effect when they act in the same direction,and inhibit each other when they act in opposite directions.     

Dynamics of bounded confidence opinion in heterogeneous social networks: Concord against partial antagonism

Bounded confidence models of opinion dynamics in social networks have been actively studied in recent years, in particular, opinion formation and extremism propagation along with other aspects of social dynamics. In this work, after an analysis of limitations of the Deffuant-Weisbuch (DW) bounded confidence, relative agreement model, we propose the mixed model that takes into account two psychological types of individuals. Concord agents (C-agents) are friendly people; they interact in a way that their opinions always get closer. Agents of the other psychological type show partial antagonism in their interaction (PA-agents). Opinion dynamics in heterogeneous social groups, consisting of agents of the two types, was studied on different social networks: Erdös-Rényi random graphs, small-world networks and complete graphs. Limit cases of the mixed model, pure C- and PA-societies, were also studied. We found that group opinion formation is, qualitatively, almost independent of the topology of networks used in this work. Opinion fragmentation, polarization and consensus are observed in the mixed model at different proportions of PA- and C-agents, depending on the value of initial opinion tolerance of agents. As for the opinion formation and arising of “dissidents”, the opinion dynamics of the C-agents society was found to be similar to that of the DW model, except for the rate of opinion convergence. Nevertheless, mixed societies showed dynamics and bifurcation patterns notably different to those of the DW model. The influence of biased initial conditions over opinion formation in heterogeneous social groups was also studied versus the initial value of opinion uncertainty, varying the proportion of the PA- to C-agents. Bifurcation diagrams showed an impressive evolution of collective opinion, in particular, radical changes of left to right consensus or vice versa at an opinion uncertainty value equal to 0.7 in the model with the PA/C mixture of population near 50/50.     

Ising model on evolution networks and its application on opinion formation

Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighbors. To describe this kind of phenomena an Ising model on evolution networks was presented and used for consensus formation and separation of opinion groups in human population. In this model the state-holding probability p and selection-rewiring probability q were introduced. The influence of this mixed dynamics of spin flips and network rewiring on the ordering behavior of the model was investigated, p hinders ordering of opinion networks and q accelerates the dynamical process of networks. Influence of q on the ordering and separating stems from its effect on average path length of networks.     

Minority persistence in agent based model using information and emotional arousal as control variables

We present detailed analysis of the behavior of an agent based model of opinion formation, using a discrete variant of cusp catastrophe behavior of single agents. The agent opinion about a particular issue is determined by its information about the issue and its emotional arousal. It is possible that for agitated agents the same information would lead to different opinions. This results in a nontrivial individual opinion dynamics. The agents communicate via messages, which allows direct application of the model to ICT based communities. We study the dependence of the composition of an agent society on the range of interactions and the rate of emotional arousal. Despite the minimal number of adjustable parameters, the model reproduces several phenomena observed in real societies, for example nearly perfectly balanced results of some highly contested elections or the fact that minorities seldom perceive themselves to be a minority.     

Voter model on adaptive networks

Voter model is an important basic model in statistical physics. In recent years, it has been more and more used to describe the process of opinion formation in sociophysics. In real complex systems, the interactive network of individuals is dynamically adjusted, and the evolving network topology and individual behaviors affect each other. Therefore, we propose a linking dynamics to describe the coevolution of network topology and individual behaviors in this paper, and study the voter model on the adaptive network. We theoretically analyze the properties of the voter model, including consensus probability and time. The evolution of opinions on dynamic networks is further analyzed from the perspective of evolutionary game. Finally, a case study of real data is shown to verify the effectiveness of the theory.     

To how many politicians should government be left?

We study opinion formation processes in small social networks. In particular we show how a group’s ability for efficient decision-making depends on its size. We adopt a threshold voter model and show that there exists a characteristic size beyond which the probability of forming internal factions-and thus absence of consensus-undergoes a qualitative change. Our work is empirically motivated by an apparent correlation between the size of a decision-making group and its performance in the particular case of national governments.     

A model of the effects of authority on consensus formation in adaptive networks: Impact on network topology and robustness

Opinions of individuals in real social networks are arguably strongly influenced by external determinants, such as the opinions of those perceived to have the highest levels of authority. In order to model this, we have extended an existing model of consensus formation in an adaptive network by the introduction of a parameter representing each agent’s level of ‘authority’, based on their opinion relative to the overall opinion distribution. We found that introducing this model, along with a randomly varying opinion convergence factor, significantly impacts the final state of converged opinions and the number of interactions required to reach that state. We also determined the relationship between initial and final network topologies for this model, and whether the final topology is robust to node removals. Our results indicate firstly that the process of consensus formation with a model of authority consistently transforms the network from an arbitrary initial topology to one with distinct measurements in mean shortest path, clustering coefficient, and degree distribution. Secondly, we found that subsequent to the consensus formation process, the mean shortest path and clustering coefficient are less affected by both random and targeted node disconnection. Speculation on the relevance of these results to real world applications is provided.     

Diffusing opinions in bounded confidence processes

We study the effects of diffusing opinions on the Deffuant et al. model for continuous opinion dynamics. Individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside an interval centered around the present opinion. We show that diffusion induces an order-disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. If the diffusion jumps are not large, clusters coalesce, so that weak diffusion favors opinion consensus. A master equation for the process described above is presented. We find that the master equation and the Monte Carlo simulations do not always agree due to finite-size induced fluctuations. Using a linear stability analysis we can derive approximate conditions for the transition between opinion clusters and the disordered state. The linear stability analysis is compared with Monte Carlo simulations. Novel interesting phenomena are analyzed.     

Opinion formation in a social network: The role of human activity

The model of opinion formation in human population based on social impact theory is investigated numerically. On the basis of a database received from the on-line game server, we examine the structure of social network and human dynamics. We calculate the activity of individuals, i.e. the relative time devoted daily to interactions with others in the artificial society. We study the influence of correlation between the activity of an individual and its connectivity on the process of opinion formation. We find that such correlations have a significant influence on the temperature of the phase transition and the effect of the mass media, modeled as an external stimulation acting on the social network.     

Opinion dynamics in networks with heterogeneous confidence and influence

We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks.     

Finding communities in directed networks by PageRank random walk induced network embedding

Community structure has been found to exist ubiquitously in many different kinds of real world complex networks. Most of the previous literature ignores edge directions and applies methods designed for community finding in undirected networks to find communities. Here, we address the problem of finding communities in directed networks. Our proposed method uses PageRank random walk induced network embedding to transform a directed network into an undirected one, where the information on edge directions is effectively incorporated into the edge weights. Starting from this new undirected weighted network, previously developed methods for undirected network community finding can be used without any modification. Moreover, our method improves on recent work in terms of community definition and meaning. We provide two simulated examples, a real social network and different sets of power law benchmark networks, to illustrate how our method can correctly detect communities in directed networks.     

The spreading of opposite opinions on online social networks with authoritative nodes

The study of opinion dynamics, such as spreading and controlling of rumors, has become an important issue on social networks. Numerous models have been devised to describe this process, including epidemic models and spin models, which mainly focus on how opinions spread and interact with each other, respectively. In this paper, we propose a model that combines the spreading stage and the interaction stage for opinions to illustrate the process of dispelling a rumor. Moreover, we set up authoritative nodes, which disseminate positive opinion to counterbalance the negative opinion prevailing on online social networking sites. With analysis of the relationship among positive opinion proportion, opinion strength and the density of authoritative nodes in networks with different topologies, we demonstrate that the positive opinion proportion grows with the density of authoritative nodes until the positive opinion prevails in the entire network. In particular, the relationship is linear in homogeneous topologies. Besides, it is also noteworthy that initial locations of the negative opinion source and authoritative nodes do not influence positive opinion proportion in homogeneous networks but have a significant impact on heterogeneous networks. The results are verified by numerical simulations and are helpful to understand the mechanism of two different opinions interacting with each other on online social networking sites.     

Markov transition probability-based network from time series for characterizing experimental two-phase flow

We generate a directed weighted complex network by a method based on Markov transition probability to represent an experimental two-phase flow. We first systematically carry out gas-liquid two-phase flow experiments for measuring the time series of flow signals. Then we construct directed weighted complex networks from various time series in terms of a network generation method based on Markov transition probability. We find that the generated network inherits the main features of the time series in the network structure. In particular, the networks from time series with different dynamics exhibit distinct topological properties. Finally, we construct two-phase flow directed weighted networks from experimental signals and associate the dynamic behavior of gas-liquid two-phase flow with the topological statistics of the generated networks. The results suggest that the topological statistics of two-phase flow networks allow quantitative characterization of the dynamic flow behavior in the transitions among different gas-liquid flow patterns.     

基于信息熵的社交网络观点演化模型

随着网络服务的发展,社交网络逐渐成为信息传播的新媒介.因此,研究网络舆情演化具有重要意义和实用价值.为了更好地研究网络舆论,在信息熵的基础上,提出了一个社交网络观点演化模型.此模型存在以下两个特点:一是可以反映个体面对正负两种观点趋向做出抉择时的心理过程;二是可以反映个体形成新观点时主观因素和客观因素的影响.在仿真实验中,讨论了舆论环境对个体观点演化的影响,初始观点和自信度对观点演化的影响,以及意见领袖对群体观点演化的影响.实验结果表明,该模型可以反映真实社交网络中个体的心理学特征,比如个体的观点形成会受到舆论环境的影响,自信的个体不愿意接受他人的观点,当意见领袖存在时群体的观点会受到影响等.