Nonlinear Opinion Dynamics Models With Stubborn Individuals Over Signed Graphs

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.

Many real-world complex systems can be modeled as dynamic networks with real-valued vertex/edge attributes. Examples include users' opinions in social networks and average speeds in a road system. When managing these large dynamic networks, compressing attribute values becomes a key requirement, since it enables the answering of attribute-based queries regarding a node/edge or network region based on a compact representation of the data. To address this problem, we introduce a lossy network compression scheme called Slice Tree (ST), which partitions a network into smooth regions with respect to node/edge values and compresses each value as the average of its region. ST applies a compact representation for network partitions, called slices, that are defined as a center node and radius distance. We propose an importance sampling algorithm to efficiently prune the search space of candidate slices in the ST construction by biasing the sampling process towards the node values that most affect the compression error. The effectiveness of ST in terms of compression error, compression rate, and running time is demonstrated using synthetic and real datasets. ST scales to million-node instances and removes up to 87% of the error in attribute values with a 103 compression ratio. We also illustrate how ST captures relevant phenomena in real networks, such as research collaboration patterns and traffic congestions.

Cluster consensus of opinion dynamics with stubborn individuals

Social media platforms have amplified opinion polarization, complicating policymaking and public sentiment management. Existing models primarily address either consensus formation or binary polarization, failing to account for the diverse, multi-polar opinion distributions observed in real-world social interactions. This work introduces a dynamic opinion model integrating individual stubbornness and opinion sensitivity, enabling the simulation of multi-opinion coexistence within social networks. It is formally proven that, under low-impact events, opinions converge to a neutral consensus under both synchronous and asynchronous updates. For high-impact events, where theoretical analysis is challenging, this work employs simulations under asynchronous updating, which better reflect real conditions. The results indicate that mixed groups may exhibit multi-state coexistence, with homogenized social relationships leading to weak opinion cohesion and social heterogeneity fostering community formation. To regulate diverse opinions in social networks, this work introduces two governance strategies designed for events with different impacts. Notably, for events with limited impact, soft opinion guidance shapes group preferences more effectively than forceful interventions. These findings offer insights for refining policy communication strategies and advancing the broader understanding of opinion dynamics in diverse societies.

In this paper, an improved Susceptible- Infected-Susceptible (SIS) epidemic spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases. This model is based on the following ideas: in social networks, the contact probability between nodes is decided by their social distances and their active degrees. The contact probability of two indirectly connected nodes is decided by the shortest path between them. Theoretical analysis and simulation experiment were conducted to evaluate the performance of this improved model. Because the proposed model is independent of the network structure, simulation experiments were done in several kinds of networks, namely the ER network, the random regular network, the WS small world network, and the BA scale-free network, in order to study the influences of certain factors have on the epidemic spreading, such as the social contact active degree, the network structure, the average degree, etc. This improved model provides an idea for studying the spreading rule of computer virus, attitudes, fashion styles and public opinions in social networks.

Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate

The introduction of social media websites touted the idea of global communication, exposing users to a worldwide audience and a diverse range of experiences, opinions, and debates. Unfortunately, studies have shown that social networks have instead contributed to growing levels of polarization in society across a wide variety of issues. Social media websites employ algorithmic filtering strategies to drive engagement, which can lead to the formation of filter bubbles and increased levels of polarization. In this paper, we introduce features of affective polarization --- feelings towards one's in-group and out-group --- into an opinion dynamics model. Specifically, we show that incorporating a negative out-group stereotype into the opinion dynamics model (1) affects the level of polarization present among agents in the network; (2) changes the effectiveness of algorithmic filtering strategies; and (3) is exacerbated by the presence of extremists in the network. Hence, the inclusion of an affective group mechanism in opinion dynamics modeling provides novel insights into the effects of algorithmic filtering strategies on the extremity of opinions in social networks.

In the conditions of digitalization, which has penetrated all spheres of human life and society, artificial intelligence (AI) and ultra-precise neural networks influence our thinking and form consumer demand and loyalty. Modern AI applications cover all the essential areas of activity: education, manufacturing, marketing, management, law, medicine, and e-commerce. The study aims to build a methodology for analyzing the influence of public opinion in social networks, particularly micro and nano influencers, through AI and machine learning on the effectiveness of companies' marketing activities. The authors studied the stages of consumer interaction with marketing profits and highlighted the role of AI technologies in each of them. They showed that public opinion was the main driving force for effective sales of products on the Internet. Based on empirical data, a strong direct relationship was found between the number of influencers and the dynamics of marketing profit: it was revealed that the correlation coefficients between the marketing profit index and the number of micro and nano influencers were 0.86–0.99 in all surveyed companies implementing AI technologies, regardless of the market niche. Based on the expert method, the company's marketing system is investigated. An integral indicator of its effectiveness is introduced, consisting of sub-indices of analysis, diffusion and marketing information management. The authors considered the factors of profit from marketing activities of five companies actively implementing AI in brand promotion, including those using the leadership opinions of influencers. The applied value of the developed methodology is the possibility of using it to construct Internet marketing strategies by companies. By permanently monitoring the relationship between the marketing profit index and the degree of brand popularization in social networks, companies can manage sales at all stages of consumer communications, optimizing the costs of influencers promoting products on different social platforms. The prospects for further research are to study the relationship between the degree of interactivity of the influencer with the audience, the content posted by it with the conversion rate and sales volumes; grouping and identification of influencers based on the clustering method.

In recent years, the spread of social networking services (SNS) has made it easier to connect with people who have similar opinions. Accordingly, similar opinions are shared within a group, while the frequency of exposure to different opinions tends to decrease. As a result, the polarization of opinion among groups is more likely to occur. Some studies have been conducted to identify the conditions under which opinion polarization occurs by simulating opinion dynamics, but specific methods for mitigating it have been poorly understood. Recently, it was found that even a few artificial perturbations inspired by the adversarial attack reverse the result in voter models, where a minority opinion becomes dominant through these perturbations. In this study, we conducted numerical simulations to determine whether it is possible to mitigate opinion polarization by adding such perturbations to the network in opinion dynamics models. The results show that opinion polarization can be mitigated by strategically generating perturbations to the weights of network links, and the effect increases as the perturbation strength parameter increases. Moreover, our analysis reveals that the effectiveness of this polarization mitigating method is enhanced in larger networks. Our results propose an effective way to prevent polarization of opinion in social networks.

We investigate opinion dynamics as a stochastic process in social networks. We introduce the stubborn agent in order to determine the impact of network structure on the emergence of consensus. Depending on the fraction of undirected long-range connections, we observe fascinatingly rich dynamical behavior and transitions from disordered to ordered states. In general, we find that the stubborn agent promotes the emergence of consensus due to the so-called “group effect” that facilitates coalescence between separated network components. Agents are also behaviorally constrained Shannon information entropy in networks. However, since agents want to evolve their opinion with Brownian motion, which may in turn impede full consensus, sufficiently frequent long-range links are in such situations crucial for the network to converge into an absorbing phase. Our experimental findings indicate that, for a large range of control parameters, our model yields stable and fluctuating polarized states.

Big data are products of human collective intelligence that are exponentially increasing in all facets of quantity, complexity, semantics, distribution, and processing costs in computer science, cognitive informatics, web-based computing, cloud computing, and computational intelligence. This paper presents fundamental big data analysis and mining technologies in the domain of social networks as a typical paradigm of big data engineering. A key principle of computational sociology known as the characteristic opinion equilibrium is revealed in social networks and electoral systems. A set of numerical and fuzzy models for collective opinion analyses is formally presented. Fuzzy data mining methodologies are rigorously described for collective opinion elicitation and benchmarking in order to enhance the conventional counting and statistical methodologies for big data analytics.

The propagation of various opinions in social networks, which influences human inter-relationships and even social structure, and hence is a most important part of social life. We have incorporated social balance into opinion propagation in social networks are influenced by social balance. The edges in networks can represent both friendly or hostile relations, and change with the opinions of individual nodes. We introduce a model to characterize the coevolutionary dynamics of these two dynamical processes on Watts-Strogatz (WS) small-world network. We employ two distinct evolution rules (i) opinion renewal; and (ii) relation adjustment. By changing the rewiring probability, and thus the small-worldness of the WS network, we found that the time for the system to reach balanced states depends critically on both the average path length and clustering coefficient of the network, which is different than other networked process like epidemic spreading. In particular, the system equilibrates most quickly when the underlying network demonstrates strong small-worldness, i.e., small average path lengths and large clustering coefficient. We also find that opinion clusters emerge in the process of the network approaching the global equilibrium, and a measure of global contrariety is proposed to quantify the balanced state of a social network.

Two models are developed for updating opinions in social networks under situations where certain beliefs might be considered to be competing. These two models represent different attitudes of people towards the perceived conflict between beliefs. In both models agents have a degree of tolerance, which represents the extent to which the agent takes into account the differing beliefs of other agents, and a degree of conflict, which represents the extent to which two beliefs are considered to be competing. Computer simulations are used to determine how the opinion dynamics are affected by the inclusion of conflict. Results show that conflict can enhance the formation of consensus within the network in certain circumstances according to one of the models.

Structural hole spanners play an important role in information diffusion. Compared with opinion leader, structural hole spanners have better location in social network to expand the scope of information diffusion. In the past, researchers focused on the evolution rules and the opinion dynamics environments to monitor public opinion and even manage public opinion to the place they want. In this paper, we propose a novel structural-hole-based approach to control public opinion in social networks (shorten for SHCPO approach). We discuss influences of opinion evolution with ordinary agents and structural hole spanners via using our improving Friedkin-Johnsen (FJ) model. We analysis evolution tendency of public opinion, which is the final consensus of public opinion via FJ model, with ordinary agents in a community and with structural hole spanners in joint communities. We conclude three kinds of connections between structural hole spanners and ordinary agents in joint communities. They are structural hole spanners connecting (1) two opinion leaders; (2) two ordinary agents; (3) one opinion leader and one ordinary agents. The three connections will lead to different conditions for opinion evolution. And then, we remove the connections if public opinion tendencies are negative in joint communities and its end-communities. It prevents public opinion of the community and one of its end-communities. It guides the public opinion tendencies of joint communities going towards positive. The experiment result shows that SHCPO approach has certain extent effects.

Our ideas, opinions and behaviors are partly shaped by our social surroundings, and in turn, our surroundings are shaped by our own ideas, opinions and behaviors. How do our beliefs and our actions change because of our interactions with others? And how does our environment change as a result? This thesis studies the interactive dynamics of intelligent agents by considering three themes. First, we study how one’s similarity to others affects the spread of behaviours and opinions in social networks and how it modifies one's social connections over time. Second, we investigate whether agents are able either individually or collectively to learn the truth if they exhibit so-called conservatism, i.e., they adopt strategies to maintain a good fit between what they come to believe after encountering new information and what they believed before. Finally, we explore whether deciding to trust or to reject pieces of information based on their internal coherence may be an effective way for an agent to filter out deceiving information and form true beliefs. Each question above is considered from a model-oriented perspective, whereby it is first transformed into a mathematically precise problem and then investigated using analytical methods or computer simulations. The formal tools employed are varied and comprise dynamic logic tools to study social network dynamics, dynamic epistemic logic tools to model belief change, and Bayesian networks and agent-based models to represent the role of cognitive biases and coherence in the evaluation of information.