Continuous opinion model in small-world directed networks

In the compromise model of continuous opinions proposed by Deffuant et al., the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance ?. In directed networks, if agent i is a neighbor of agent j,j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions 〈F〉 and their distribution as a function of ? and of the network structural disorder. In directed networks 〈F〉 exhibits a rich structure, being larger than in undirected networks for higher values of ?, and smaller for lower values of ?.     

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.     

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.     

External activation promoting consensus formation in the opinion model with interest decay

We put forward an opinion model that considers internal decay and external activation or deactivation. Agents may withdraw from the discussion, meanwhile, these inactive agents are likely to be motivated by active neighbors. In addition, external influence from outside circumstances is added to the population. We focus on the majority rule of opinion exchange. Our investigations reveal under the impact of external circumstances, the system evolves to different stable states. One opinion can finally be made dominant when the internal motivation is large sufficiently. However, without external activation, consensus is hardly reached in the system with interest decay.     

The effects of nonlinear interactions and network structure in small group opinion dynamics

We present a model of opinion dynamics in social networks in which an individual's opinion evolves under the action of (i) a linear force which tends to restore the opinion back towards the individual's natural bias that is his or her initial opinion and (ii) a nonlinear coupling with other individuals which acts to bring opinions closer together but wanes for high opinion discrepancies. Bifurcation analysis for the case of a two-person group shows that a critical value for the difference in natural biases exists which demarcates regimes of qualitatively different behavior. For low to moderate natural bias differences, the dynamics are qualitatively similar to linear theory. For high bias differences, the system takes on a binary nature and is marked by discontinuous transitions between deadlock and consensus as well as hysteresis as the coupling is varied. The coupling required to force consensus grows extremely rapidly with the natural bias difference indicating that trying to achieve group consensus solely via increasing the communications rate becomes fruitless as the biases become extremely divergent. We also show that, for high bias differences, a triad broker network topology can reduce group discord more effectively than a clique, contrary to linear theory.     

Social networks: Ideas for future research from the vantage point of political science

In this short piece, Bunce and Csanadi draw upon their expertise in political science and political economy to offer some observations about the analysis of social networks. Using both examples and questions they highlight the importance of structural variations in networks, including differences in the motivations behind network formation; the subsequent development of networks, including extension, contraction and duration; and the effects of individual decision-makers on network dynamics and, at the same time, the effects of network structure and dynamics on individual decision-makers.     

Transnational networks,diffusion dynamics,and electoral revolutions in the postcommunist world

Since 1996, eight elections have taken place in postcommunist Europe and Eurasia that have replaced illiberal with liberal governments. There is ample evidence that these “electoral revolutions” reflected the cross-national diffusion of a distinctive model of regime change that was developed elsewhere and that was designed to promote democratization in authoritarian political contexts featuring semi-competitive elections. This electoral model spread throughout the postcommunist region because of both shared perceptions by opposition groups of similar local conditions and the existence of transnational democracy promotion networks that included local, regional and American participants. As these revolutions spread, however, they were less successful in carrying through democratic change-in part because local conditions were less supportive and in part because authoritarian leaders and their international allies were both forewarned and forearmed.     

Influence of a network structure on the network effect in the communication service market

In this study, we analyze the network effect in a model of a personal communication market, by using a multi-agent based simulation approach. We introduce into the simulation model complex network structures as the interaction patterns of agents. With complex network models, we investigate the dynamics of a market in which two providers are competing. We also examine the structure of networks that affect the complex behavior of the market. By a series of simulations, we show that the structural properties of complex networks, such as the clustering coefficient and degree correlation, have a major influence on the dynamics of the market. We find that the network effect is increased if the interaction pattern of agents is characterized by a high clustering coefficient, or a positive degree correlation. We also discuss a suitable model of the interaction pattern for reproducing market dynamics in the real world, by performing simulations using real data of a social network.     

Trust in the CODA model: Opinion dynamics and the reliability of other agents

A model for the joint evolution of opinions and how much the agents trust each other is presented, using the framework of the Continuous Opinions and Discrete Actions (CODA) model. Instead of a fixed probability that the other agents will decide in the favor of the best choice, each agent considers that other agents might be one of two types: trustworthy or untrustworthy. Each agent its opinion and also the probability for each one of the other agents it interacts with being trustworthy. The dynamics of opinions and the evolution of the trust between the agents are studied. Clear evidences of the existence of two phases, one with strong polarization and the other tending to agreement, are observed. The transition shows signs of being a first-order transition. This happens despite the fact that the trust network evolves much slower than the opinion on the central issue.     

A study of the spreading scheme for viral marketing based on a complex network model

Buzzword-based viral marketing, known also as digital word-of-mouth marketing, is a marketing mode attached to some carriers on the Internet, which can rapidly copy marketing information at a low cost. Viral marketing actually uses a pre-existing social network where, however, the scale of the pre-existing network is believed to be so large and so random, so that its theoretical analysis is intractable and unmanageable. There are very few reports in the literature on how to design a spreading scheme for viral marketing on real social networks according to the traditional marketing theory or the relatively new network marketing theory. Complex network theory provides a new model for the study of large-scale complex systems, using the latest developments of graph theory and computing techniques. From this perspective, the present paper extends the complex network theory and modeling into the research of general viral marketing and develops a specific spreading scheme for viral marking and an approach to design the scheme based on a real complex network on the QQ instant messaging system. This approach is shown to be rather universal and can be further extended to the design of various spreading schemes for viral marketing based on different instant messaging systems.     

A social network model of investment behaviour in the stock market

To consider the psychological factors that impact market valuation, a model is formulated for investment behaviour of traders whose decisions are influenced by their trusted peers’ behaviour. The model is implemented and several different “trust networks” are tested. Simulation results demonstrate that real life trust networks can significantly delay the stabilisation of a market.     

The co-evolution of cultures,social network communities,and agent locations in an extension of Axelrod’s model of cultural dissemination

We introduce a variant of the Axelrod model of cultural dissemination in which agents change their physical locations, social links, and cultures. Numerical simulations are used to investigate the evolution of social network communities and the cultural diversity within and between these communities. An analysis of the simulation results shows that an initial peak in the cultural diversity within network communities is evident before agents segregate into a final configuration of culturally homogeneous communities. Larger long-range interaction probabilities facilitate the initial emergence of culturally diverse network communities, which leads to a more pronounced initial peak in cultural diversity within communities. At equilibrium, the number of communities, and hence cultures, increases when the initial cultural diversity increases. However, the number of communities decreases when the lattice size or population density increases. A phase transition between two regimes of initial cultural diversity is evident. For initial diversities below a critical value, a single network community and culture emerges that dominates the population. For initial diversities above the critical value, multiple culturally homogeneous communities emerge. The critical value of initial diversity at which this transition occurs increases with increasing lattice size and population density and generally with increasing absolute population size. We conclude that larger initial diversities promote cultural heterogenization, while larger lattice sizes, population densities, and in fact absolute population sizes promote homogenization.     

Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks

We investigate the effects of delaying the time to recovery (delayed recovery) and of nonuniform transmission on the propagation of diseases on structured populations. Through a mean-field approximation and large-scale numerical simulations, we find that postponing the transition from the infectious to the recovered states can largely reduce the epidemic threshold, therefore promoting the outbreak of epidemics. On the other hand, if we consider nonuniform transmission among individuals, the epidemic threshold increases, thus inhibiting the spreading process. When both mechanisms are at work, the latter might prevail, hence resulting in an increase of the epidemic threshold with respect to the standard case, in which both ingredients are absent. Our findings are of interest for a better understanding of how diseases propagate on structured populations and to a further design of efficient immunization strategies.     

A comparison of coal supply-demand in China and in the US based on a network model

Through analysis the actual coal supply and demand in the US and China, the properties of the coal supply-demand market in both countries are investigated based on the energy supply-demand network. The validity of our model is verified by comparing numerical results with empirical results. The comparison of empirical results and the comparison of coal network model parameters between in the US and in China reveal the essence of the internal differences and similarities of coal supply and demand in these two countries. The third stage of China＇s coal network was close to that of the US in 1995, indicating that the evolutional situation of China＇s coal market begins to transit to an oligopolistic type. Finally, suggestions for China＇s coal supply-demand strategy are put forward.     

Ranking the spreading influence of nodes in complex networks: An extended weighted degree centrality based on a remaining minimum degree decomposition

Ranking the spreading influence of nodes is crucial for developing strategies to control the spreading process on complex networks. In this letter, we define, for the first time, a remaining minimum degree (RMD) decomposition by removing the node(s) with the minimum degree iteratively. Based on the RMD decomposition, a weighted degree (WD) is presented by utilizing the RMD indices of the nearest neighbors of a node. WD assigns a weight to each degree of this node, which can distinguish the contribution of each degree to the spreading influence. Further, an extended weighted degree (EWD) centrality is proposed by extending the WD of the nearest neighbors of a node. Assuming that the spreading process on networks follows the Susceptible-Infectious-Recovered (SIR) model, we perform extensive experiments on a series of synthetic and real networks to comprehensively evaluate the performance of EWD and other eleven representative measures. The experimental results show that EWD is a relatively efficient measure in running efficiency, it exposes an advantage in accuracy in the networks with a relatively small degree heterogeneity, as well as exposes a competitive performance in resolution.     

Effect of a monomeric sequence on the structure of hydrated Nafion in the sandwich model and solvent dynamics in nano-channels: a molecular dynamic study

Molecular dynamics simulations are performed to obtain insight into the structural properties of hydrated Nafion using the sandwich model of the polymer membrane. It is shown that a larger distance between the sulfonate groups of a chain leads to the polymer forming a better inverted micelles structure. Water– and hydronium–polymer interfaces are investigated. Comparing our results with others indicates that, from the perspective of distance, the formation of shells of water and hydronium ions is independent of the model and monomer type, but depends on both if the coordination number is considered. The behaviour of water molecules and hydronium ions is also studied dynamically. Our survey shows that there is an increasing jump in the diffusion coefficient of water at a certain distance between the sulfonate groups of a chain, which then tends to change slightly. Such behaviour is discussed on the basis of density, the available space, as well as the loss of one translational degree of freedom of the water molecules at larger distances. The diffusion coefficient for the hydronium ions was also determined to be much smaller than that for water (by 3.5–6.1 times). The diffusion coefficient of the hydronium ions shows a declining jump at a certain distance between the sulfonate groups of a chain, but the jump is not significant as that for the water molecules.     

Solution of the unanimity rule on exponential, uniform and scalefree networks: A simple model for biodiversity collapse in foodwebs

We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this state. The solutions for exponential and uniform networks are exact, the analytical approximation for the scalefree case is in perfect agreement with simulation results. We use these solutions to provide a theoretical understanding for biodiversity loss in experimental data of foodwebs, which is available for the three network types discussed. The model allows in principle to estimate the critical value of species that have to be removed from the system to induce a complete diversity collapse.     

Effects of particle size, shape and crystal structure on the formation energy of Schottky vacancies in free-standing metal nanoparticles: A model study

A simplified model based on cohesive energy is proposed to estimate the formation energy of Schottky vacancies (VFE) in free-standing metal nanoparticles with BCC and FCC crystal structures. To study the effect of particle size and shape, the surface energy, elastic contraction and average coordination number of particles at the surface and core was considered. It is shown that the energy of vacancy formation in FCC nanoparticles increases with decreasing the size while the effect of particle shape (sphere, cubic and icosahedral) is marginal. In spite of this behavior, BCC nanoparticles exhibit a critical particle size at around 25 Å, at which a minimum VFE is attained. Additionally, the energy of vacancy formation is notably lower for BCC nanoparticles with cubic shape than spherical ones. The application of the developed model is shown for free-standing Fe and Cu nanoparticles.