Opinion formation driven by PageRank node influence on directed networks

We study a two states opinion formation model driven by PageRank node influence and report an extensive numerical study on how PageRank affects collective opinion formations in large-scale empirical directed networks. In our model the opinion of a node can be updated by the sum of its neighbor nodes' opinions weighted by the node influence of the neighbor nodes at each step. We consider PageRank probability and its sublinear power as node influence measures and investigate evolution of opinion under various conditions. First, we observe that all networks reach steady state opinion after a certain relaxation time. This time scale is decreasing with the heterogeneity of node influence in the networks. Second, we find that our model shows consensus and non-consensus behavior in steady state depending on types of networks: Web graph, citation network of physics articles, and LiveJournal social network show non-consensus behavior while Wikipedia article network shows consensus behavior. Third, we find that a more heterogeneous influence distribution leads to a more uniform opinion state in the cases of Web graph, Wikipedia, and Livejournal. However, the opposite behavior is observed in the citation network. Finally we identify that a small number of influential nodes can impose their own opinion on significant fraction of other nodes in all considered networks. Our study shows that the effects of heterogeneity of node influence on opinion formation can be significant and suggests further investigations on the interplay between node influence and collective opinion in networks.Comment: 10 pages, 6 figures. Published in Physica A 436, 707-715 (2015

Consensus formation on adaptive networks

The structure of a network can significantly influence the properties of the dynamical processes which take place on them. While many studies have been devoted to this influence, much less attention has been devoted to the interplay and feedback mechanisms between dynamical processes and network topology on adaptive networks. Adaptive rewiring of links can happen in real life systems such as acquaintance networks where people are more likely to maintain a social connection if their views and values are similar. In our study, we consider different variants of a model for consensus formation. Our investigations reveal that the adaptation of the network topology fosters cluster formation by enhancing communication between agents of similar opinion, though it also promotes the division of these clusters. The temporal behavior is also strongly affected by adaptivity: while, on static networks, it is influenced by percolation properties, on adaptive networks, both the early and late time evolution of the system are determined by the rewiring process. The investigation of a variant of the model reveals that the scenarios of transitions between consensus and polarized states are more robust on adaptive networks.Comment: 11 pages, 14 figure

The Dynamics of Public Opinion in Complex Networks

This paper studies the problem of public opinion formation and concentrates on the interplays among three factors: individual attributes, environmental influences and information flow. We present a simple model to analyze the dynamics of four types of networks. Our simulations suggest that regular communities establish not only local consensus, but also global diversity in public opinions. However, when small world networks, random networks, or scale-free networks model social relationships, the results are sensitive to the elasticity coefficient of environmental influences and the average connectivity of the type of network. For example, a community with a higher average connectivity has a higher probability of consensus. Yet, it is misleading to predict results merely based on the characteristic path length of networks. In the process of changing environmental influences and average connectivity, sensitive areas are discovered in the system. By sensitive areas we mean that interior randomness emerges and we cannot predict unequivocally how many opinions will remain upon reaching equilibrium. We also investigate the role of authoritative individuals in information control. While enhancing average connectivity facilitates the diffusion of the authoritative opinion, it makes individuals subject to disturbance from non-authorities as well. Thus, a moderate average connectivity may be preferable because then the public will most likely form an opinion that is parallel with the authoritative one. In a community with a scale-free structure, the influence of authoritative individuals keeps constant with the change of the average connectivity. Provided that the influence of individuals is proportional to the number of their acquaintances, the smallest percentage of authorities is required for a controlled consensus in a scale free network. This study shows that the dynamics of public opinion varies from community to community due to the different degree of impressionability of people and the distinct social network structure of the community.Public Opinion, Complex Network, Consensus, Agent-Based Model

From Social Network (Centralized vs. Decentralized) to Collective Decision-Making (Unshared vs. Shared Consensus)

Relationships we have with our friends, family, or colleagues influence our personal decisions, as well as decisions we make together with others. As in human beings, despotism and egalitarian societies seem to also exist in animals. While studies have shown that social networks constrain many phenomena from amoebae to primates, we still do not know how consensus emerges from the properties of social networks in many biological systems. We created artificial social networks that represent the continuum from centralized to decentralized organization and used an agent-based model to make predictions about the patterns of consensus and collective movements we observed according to the social network. These theoretical results showed that different social networks and especially contrasted ones – star network vs. equal network - led to totally different patterns. Our model showed that, by moving from a centralized network to a decentralized one, the central individual seemed to lose its leadership in the collective movement's decisions. We, therefore, showed a link between the type of social network and the resulting consensus. By comparing our theoretical data with data on five groups of primates, we confirmed that this relationship between social network and consensus also appears to exist in animal societies

Opinion influence and evolution in social networks: a Markovian agents model

In this paper, the effect on collective opinions of filtering algorithms managed by social network platforms is modeled and investigated. A stochastic multi-agent model for opinion dynamics is proposed, that accounts for a centralized tuning of the strength of interaction between individuals. The evolution of each individual opinion is described by a Markov chain, whose transition rates are affected by the opinions of the neighbors through influence parameters. The properties of this model are studied in a general setting as well as in interesting special cases. A general result is that the overall model of the social network behaves like a high-dimensional Markov chain, which is viable to Monte Carlo simulation. Under the assumption of identical agents and unbiased influence, it is shown that the influence intensity affects the variance, but not the expectation, of the number of individuals sharing a certain opinion. Moreover, a detailed analysis is carried out for the so-called Peer Assembly, which describes the evolution of binary opinions in a completely connected graph of identical agents. It is shown that the Peer Assembly can be lumped into a birth-death chain that can be given a complete analytical characterization. Both analytical results and simulation experiments are used to highlight the emergence of particular collective behaviours, e.g. consensus and herding, depending on the centralized tuning of the influence parameters.Comment: Revised version (May 2018

Vanishing threshold in depolarization of correlated opinions on social networks

The process of opinion depolarization is assumed to be mediated through social networks, where interacting individuals reciprocally exert social influence leading to a consensus. While network topology plays a decisive role in many networked dynamical processes, its effect on depolarization dynamics remains unclear. Here, we show that, in a recently proposed opinion depolarization model, the threshold of the transition from correlated and polarized opinions to consensus can vanish on heterogeneous social networks. Our theoretical findings are validated by running numerical simulations on both synthetic and real social networks, confirming that a polarized yet heterogeneously connected population can reach a consensus even in the presence of weak social influence.Comment: Main paper (6 pages) + Supplemental Material (6 pages