Abstract: Disagreement and conflict are a fact of social life. However, negative interactions are rarely explicitly declared and recorded and this makes them hard for scientists to study. We use complex network methods to investigate patterns in the timing and configuration of contributions to collaboration communities in order to find evidence for negative interactions. We analyze sequences of reverts of article edits to Wikipedia, the largest online encyclopedia, and investigate how often and how fast they occur compared to a null model that randomizes the order of actions to remove any systematic clustering. Our results suggest that Wikipedia editors systematically revert the same person, revert back their reverter, and come to defend a reverted editor. We further relate these interactions to the status of the involved editors. Our findings reveal that certain social dynamics that have not been previously explored might underlie the knowledge collection practice conducted on Wikipedia. We also devise an Agent-Based-Model of common value production. Our opinion dynamics model is capable of explnaning the impirical observations and also allowe us to go beyond and test different scenarios. for instanse, we particularly study the role of extreamist editors and show that the consensus can only be reached if extremist groups can take actively part in the discussion and if their views are also represented in the common product at least temporarily. We also consider the effects of banning editors with unconventional opinions and show that banning problematic editors mostly hinders the consensus as it delays discussion and thus the whole consensus building process.

Abstract: The underlying mechanisms for the conflict and coordination in Wikipedia editing have attracted enormous research attention. A noticeable model is proposed by Török and colleagues, which shows the random renewal of agents or editors is the key source of persistent controversy during the editing of a Wikipedia article. In this work, a modified model is proposed, based on the hypothesis that the contingent-activation of zealots with extremist opinions is substitutable to the renewal of agents in generating controversies. Numerical simulations reveal that the proposed model can basically reproduce the three identified regimes of conflict in Wikipedia editing, as well as the transitions between them. With the presence of a small number of contingently-activated zealots, the system would gradually transit from the “single conflict” regime to the “plateaus of consensus” and then to the “uninterrupted controversy” regime, as the agents’ tolerance threshold to the medium opinion decreases and the zealots’ activation rate increases. What's more, richer phenomena can be observed in the proposed model. Especially, the inclusion of contingently-activated zealots significantly influences the conflict dynamics. At different rates of fraction of zealots, the combination of tolerance threshold and zealot activation rate may have different modes of influence on the density of conflict. When the fraction of zealots increases, it can surprisingly be observed that the regime of "uninterrupted controversy" vanishes, while the system has two remaining phases, i.e. “single conflict” and “plateaus of consensus”. Thus the overall dynamics depicted in the proposed model is quite different from that in the original collective Wikipedia editing model.

Abstract: The role of social media such as Twitter in today’s political elections has become crucial. However, the ever-increasing amount of data available has rendered the task of identifying the real opinion leaders and understanding their impact on the social community extremely difficult. Using an unique large-scale dataset of tweets concerning the US 2016 election primaries, we investigate the temporal social network formed by the interactions among millions of Twitter users. Using the Collective Influence (CI) algorithm introduced by Morone & Makse, Nature, 524, 65 (2015), we are able to identify the most influential users of the social network, who are able to spread information the most efficiently to the whole network. The CI algorithm finds the minimal set of influencers by solving the optimal percolation in the network. The political opinion of Twitter influencers is determined using a combination of natural language processing of the tweet contents, machine learning classification and analysis of the hashtags co-occurrence network. Using this framework we are able to follow the dynamic of the influencers and to understand their role in the diffusion of opinion. The influencers tend to have stronger opinions than average Twitter users, and shifts in their sentiment appear to predict election results in primaries.

Abstract: We proposed a new model, which capture the main difference between information and opinion spreading in complex networks. In the case of information spreading additional exposure to certain information has a small effect. Contrary, when an actor is exposed to 2 opinioned actors the probability to adopt the opinion is significant higher than in the case of contact with one such actor (called by J. Kleinberg "the 0-1-2 effect"). In each time step if an actor does not have an opinion, we randomly choose 2 his network neighbors. If one of them has an opinion, the actor adopts opinion with some low probability, if two – with a higher probability. Opinion spreading was simulated on different real world social networks and similar random scale-free networks. The results show that small world structure has a crucial impact on tipping point time. The "0-1-2" effect causes a significant difference between ability of the actors to start opinion spreading. Actor is an opinion leader according to his topological position in the network. Known characteristics of an actor in a network cannot indicate if he or she is a potential opinion leader. It's clear that an opinion leader must not have a low degree and must have a high clustering coefficient value. To become an opinion leader, a special position of an actor in the network is needed and this position is not a local property of the actor.