Opinion Dynamics on Complex Networks with Communities

The Ising or Potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in the scale-free networks with the tunable strength （noted by Q） of community structure. In the Sznajd model, the opinion or state of any spins can only be changed by the influence of neighbouring pairs of similar connection spins. Such pairs can polarize their neighbours. Using asynchronous updating, it is found that the smaller the community strength Q, the larger the slope of the exponential relaxation time distribution. Then the effect of the initial upspin concentration p as a function of the final all up probability E is investigated by taking different initialization strategies, the random node-chosen initialization strategy has no difference under different community strengths, while the strategies of community node-chosen initialization and hub node-chosen initialization are different in fina/probability under different Q, and the latter one is more effective in reaching final state.     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can besorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemicmodels on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals＇ relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each ease. Finally, we present numerical simulations for each case to verify our results.     

Three-State Opinion Model on Complex Topologies

We investigate opinion diffusion on complex networks and the interplay between the existence of neutral opinion states and non-trivial network structures. For this purpose, we apply a three-state opinion model based on magnetic-like interactions to modular complex networks, both synthetic and real networks extracted from Twitter. The model allows for tuning the contribution of neutral agents using a neutrality parameter. We also consider social agitation, encoded as a temperature, that accounts for random opinion changes that are beyond the agent neighborhood opinion state. Using this model, we study which topological features influence the formation of consensus, bipartidism, or fragmentation of opinions in three parties, and how the neutrality parameter and the temperature interplay with the network structure.     

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.     

Opinion Spreading with Mobility on Scale-Free Networks

A continuum opinion dynamic model is presented based on two rules. The first one considers the mobilities of the individuals, the second one supposes that the individuals update their opinions independently. The results of the model indicate that the bounded confidence εc, separating consensus and incoherent states, of a scale-free network is much smaller than the one of a lattice. If the system can reach the consensus state, the sum of all individuals＇ opinion change Oc（t） quickly decreases in an exponential form, while if it reaches the incoherent state finally, Oc（t） decreases slowly and has the punctuated equilibrium characteristic.     

Geographical Effects on Complex Networks

We investigate how the geographical structure of a complex network affects its network topology, synchronization and the average spatial length of edges. The geographical structure means that the connecting probability of two nodes is related to the spatial distance of the two nodes. Our simulation results show that the geographical structure changes the network topology. The synchronization tendency is enhanced and the average spatial length of edges is enlarged when the node can randomly connect to the further one. Analytic results support our understanding of the phenomena.     

Geographical Effects on Complex Networks

We investigate how the geographical structure of a complex network affects its network topology, synchronization and the average spatial length of edges. The geographical structure means that the connecting probability of two nodes is related to the spatial distance of the two nodes. Our simulation results show that the geographical structure changes the network topology. The synchronization tendency is enhanced and the average spatial length of edges is enlarged when the node can randomly connect to the further one. Analytic results support our understanding of the phenomena.     

Epidemic Diffusion on Complex Networks

Both diffusion and epidemic are well studied in the stochastic systems and complex networks, respectively. Here we combine these two fields and study epidemic diffusion in complex networks. Instead of studying the threshold of infection, which was focused on in previous works, we focus on the diffusion behayiour. We find that the epidemic diffusion in a complex network is an anomalous superdiffusion with varying diffusion exponent and that γ is influenced seriously by the network structure, such as the clustering coefficient and the degree distribution. Numerical simulations have confirmed the theoretical predictions.     

Opinion Dynamics on Networks under Correlated Disordered External Perturbations

We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The fluctuations (variance and correlations) in the external perturbations are shown to reduce the impact of the external influence by increasing the critical threshold needed for the bimodal distribution of opinions to appear. The external fluctuations also have the surprising effect of driving voters towards biased opinions. Furthermore, the first and second moments of the external perturbations are shown to affect the first and second moments of the vote-share distribution. This is shown analytically in the mean field limit, and confirmed numerically for fully connected networks and other network topologies. Studying the dynamic response of complex systems to disordered external perturbations could help us understand the dynamics of a wide variety of networked systems, from social networks and financial markets to amorphous magnetic spins and population genetics.     

Properties of Bottleneck on Complex Networks

The traffic bottleneck plays a key role in most of the natural and artificial network. Here we present a simply model for bottleneck dynamical characteristics consideration the reliability on the complex network by taking into account the network topology characteristics and system size. We find that there is a critical rate of flow generation below which the network traffic is free but above which traffic congestion occurs. Also, it is found that random networks have larger critical flow generating rate than scale free ones. Analytical results may be practically useful for designing networks, especially for the urban traffic network.     

Multiple Partial Attacks on Complex Networks

We numerically investigate the effect of four kinds of partial attacks of multiple targets on the Barabási Albert （BA） scale-free network and the Erdos-Rényi （ER） random network. Comparing with the effect of single target complete knockout we find that partial attacks of multiple targets may produce an effect higher than the complete knockout of a single target on both BA scale-free network and ER random network. We also find that the BA scale-free network seems to be more susceptible to multi-target partial attacks than the ER random network.     

Self-Organized Optimization of Transport on Complex Networks

We propose a self-organized optimization mechanism to improve the transport capacity of complex gradient networks.We find that,regardless of network topology,the congestion pressure can be strongly reduced by the self-organized optimization mechanism.Furthermore,the random scale-free topology is more efficient to reduce congestion compared with the random Poisson topology under the optimization mechanism.The reason is that the optimization mechanism introduces the correlations between the gradient field and the local topology of the substrate network.Due to the correlations,the cutoff degree of the gradient network is strongly reduced and the number of the nodes exerting their maximal transport capacity consumedly increases.Our work presents evidence supporting the idea that scale-free networks can efficiently improve their transport capacity by selforganized mechanism under gradient-driven transport mode.     

A Generalized Voter Model on Complex Networks

We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter α which sets the likelihood of the higher degree node giving its state to the other node. Traditional voter model behaviors can be recovered within the model, as well as the invasion process. We find that on a complete bipartite network, the voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of α, exit time is dominated by diffusive drift of the system state, but as the high-degree nodes become more influential, the exit time becomes dominated by frustration effects dependent on the exact topology of the network.     

Dynamic Parameter Calibration Framework for Opinion Dynamics Models

In the past decade, various opinion dynamics models have been built to depict the evolutionary mechanism of opinions and use them to predict trends in public opinion. However, model-based predictions alone cannot eliminate the deviation caused by unforeseeable external factors, nor can they reduce the impact of the accumulated random error over time. To solve this problem, we propose a dynamic framework that combines a genetic algorithm and a particle filter algorithm to dynamically calibrate the parameters of the opinion dynamics model. First, we design a fitness function in accordance with public opinion and search for a set of model parameters that best match the initial observation. Second, with successive observations, we tracked the state of the opinion dynamic system by the average distribution of particles. We tested the framework by using several typical opinion dynamics models. The results demonstrate that the proposed method can dynamically calibrate the parameters of the opinion dynamics model to predict public opinion more accurately.     

Synchronization in Triangled Complex Networks

Using a tunable clustering coefficient model without changing the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.     

Natural Connectivity of Complex Networks

The concept of natural connectivity is reported as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It is shown that the natural connectivity can be derived mathematically from the graph spectrum as an average eigenvalue and that it changes strictly monotonically with the addition or deletion of edges. By comparing the natural connectivity with other typical robustness measures within a scenario of edge elimination, it is demonstrated that the naturM connectivity has an acute discrimination which agrees with our intuition.     

Chaos Synchronization in Complex Networks

We employ several simple numerical experiments to show that the statements that short mean path length or low heterogeneity enhances synchronizability in complex networks could be misleading. Furthermore, we point out that the impacts of the structural parameters on the synchronizability are complicated even if we could change one structural parameter independently.     

Hierarchical Characterization of Complex Networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.