Abstract: Language trees have been observed to mirror gene trees from local to global scales. This suggests that languages and genes evolve in tandem as the communities that carry them split and diverge, but this model is inconsistent with the widespread mobility often observed between communities. Instead we require a model that explains correlations between genes and languages, while accounting for variable rates of migration and language adoption by individuals. Here we show that the critical variable is that human movements are not random, but highly structured. In the first study of its kind, finely resolved co-phylogenies of languages and genes on a multilingual Indonesian island reveal that marriage systems explain why language trees predict gene trees. Communities of related individuals speaking the same language can persist for many generations, while the languages they speak change or are replaced.

Abstract: In the 90s Robert Axelrod have proposed the canonical model of social interactions [1] explaining one of possible and important mechanisms of dissemination of culture. He have found that depending on initial conditions the system can end up in one of two states: ordered with global culture or disordered with many small subcultures. The dynamics of this model captured complexities of real interactions between people, but the square lattice which was considered is far from satisfying reflection of real-world social networks. Others have studied Axelrod's model deeper on complex networks and it turned out that the structure can have fundamental influence on the behavior of the system. Maxi San Miguel et. al. [2] made the next step by exploring the model of social interactions on coevolving random networks and finding two phase transitions with interesting properties. Unfortunately social networks are as far from randomness as from regularity. In our work we introduce four extensions changing the mechanism of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment in scientist or actors collaborations and friendship formation in everyday relations. Numerical simulations show that proposed dynamics can lead to power-law distribution of the degree of nodes and high value of clustering coefficient, still keeping the small-world effect in three models. All models are characterized by two phase transitions of different nature. We find new and universal characteristics of the second transition point - abrupt increase of the clustering coefficient, due to the formation of many small complete subgraphs inside the network. [1] R. Axelrod, The dissemination of culture, J. Conflict Res. 41, 203 (1997) [2] F. Vazquez, J. C. Gonzalez-Avella, V. M. Eguíluz, M. San Miguel, Time-scale competition leading to fragmentation and recombination transitions in the coevolution of network and states, Phys. Rev. E 76, 046120 (2007)

Abstract: The famous Zipf law states that the frequency of a word in a text is roughly proportional to the inverse of its rank. When the text is shuffled, this Zipf's law however remains unchanged. In this article, we aim to specify a universal law underlying arrangement of words by using an interval analysis. For each text, we study the fraction of rare words that have ranks above some threshold Q and the length of the return intervals between them. We focus on the frequency of intervals of length r from which we derive the cumulated probability S_Q(r) that the length of an interval is above r, and also the autocorrelation function C_Q(s) of the intervals. When the arrangement of the text is destroyed by shuffling, S_Q(r) is a simple exponential and C_Q(s) is zero for s above zero. We first analyze six long masterpieces in English, French, German, Chinese and Japanese and find that in all texts, for large enough Q values, S_Q(r) follows a clear Weibull function, with its exponent close to 0.7. The return intervals themselves are arranged in a self-similar long-range correlated fashion, where the autocorrelation function C_Q(s) follows a power law, with an exponent between 0.2 and 0.4. These features lead to a pronounced clustering of rare words in the text. We then show how our findings apply on a large scale through 1109 single-author texts. Our results reveal that the arrangement of a text quantified by the return intervals between the words above certain ranks Q, is surprisingly universal, obeying the same laws for all languages considered. We argue that the source of this universality is the human brain.

Abstract: In a complex social system, behavior is often prescribed and regulated by hundreds, or even thousands, of interacting norms. Yet it is individuals that must learn norms—through interaction, exploration heuristics, and local peer influence—and individuals that decide when and how to use them. Little is known about this crucial process. How do individuals selectively, and collectively, navigate and utilize the norms of their social system, and what impact does this process have on that system's development? We provide new answers to this question, by tracking how people use and invoke norms in a real world social system: the English-language Wikipedia. As a community-managed knowledge commons, Wikipedia relies on its norms for governance; they form shared expectations for content creation and conflict resolution. Norms are invoked both directly and indirectly in discussions and arguments on the encyclopedia’s “talk” pages. We sample approximately 11,000 Wikipedia editors and use the detailed, and dated, log of their talk page edits to track the norms each editor references over the course of 15 years. Combined with prior work on Wikipedia’s norm network, this allows us to infer the coarse-grained mental representations individuals use, to test mechanisms for norm learning, to determine how an individual’s invocation of norms is influenced by context, and to test the “moral tribes” hypothesis: that individuals cluster together in distinct regions of the larger norm network.

Abstract: The present study is the first of its kind to employ a complex dynamical systems approach to bridging the gap between social psychological research on stigma, and embodied cognition more broadly. Specifically, we extended current understanding of consequences for revealing devalued identities in close and professional relationships by examining the dynamic structure of movement and language during such disclosures. Using a range of nonlinear time series techniques, including fractal, multifractal, and continuous and categorical recurrence analyses, we investigated the role of antecedent motivational systems on the differential effectiveness of disclosure processes. Participants with concealable stigmatized identities were asked to prepare two disclosure letters to individuals that were unaware of their identity, one to a close friend or relative and the other to a professional colleague. Motivational orientation was manipulated so that half of participants were asked to focus on positive outcomes for the disclosures (approach goals) and the remaining participants were asked to focus on avoiding negative outcomes within the disclosure (avoidant goals). Participants read each letter aloud and their behavior was recorded using multiple motion tracking methods in addition to traditional audio video recordings. Results demonstrate differences in the dynamics of both human movement (i.e., postural sway complexity) and in language usage and form as a function of motivational goals and perceiver for disclosure. Discussion will include implications and future directions for how the differential dynamics of disclosure influence perceptions and may be embodied in the perceiver via complexity matching.

Abstract: The role of committed minorities in shaping public opinion has been recently addressed with the help of multi-agent models. However, previous studies focused on homogeneous populations where zealots stand out only for their stubbornness. Here, we consider the more general case in which individuals are characterized by different propensities to communicate. In particular, we correlate commitment with a higher tendency to push an opinion, acknowledging the fact that individuals with unwavering dedication to a cause are also more active in their attempts to promote their message. We show that these activists are not only more efficient in spreading their message but that their efforts require an order of magnitude fewer individuals than a randomly selected committed minority to bring the population over to a new consensus. Finally, we address the role of communities, showing that partisan divisions in the society can make it harder for committed individuals to flip the status-quo social consensus.

Abstract: The utterance selection model (USM) for language change (Baxter et al. 2006) is a stochastic agent-based model developed to simulation language change. In this model, agents are vertices of a graph and interact along its edges by stochastically producing utterances and learning from them. The dynamics of such an agent-based model is defined at the agent level and it is usually difficult to deduce the average dynamics of the complete population. In the original paper, the authors derived a continuous time limit in the form of a Fokker-Planck equation. This limit is only valid for a restricted set of parameters. In this talk, I will derive a new continuous time limit of the USM, which has no constraints on parameters and use it to derive a coarse-grained population level approximation of the dynamics. This approximation is a stochastic version of the heterogeneous mean field approximation. Using this approximation, I will characterize the dynamics of the USM at the population level. In particular, I will show that the population dynamics of the system can mainly be captured by three parameters. The analysis also reveals a finite-size effect in the dynamics.

Abstract: Facial emotions are believed to be very expressive social stimuli; hence significant amount of efforts have been made within the past two decades to detect, study and analyze these emotions in a way to reveal specific human behaviors and characteristics, in this paper we aim to decode some of the detected facial emotions on political leaders in a way to find potential correlations between their facial expressions and impacts on voter preference decisions in the United States, we study facial emotions detected on images of selected Republican and Democratic presidential candidates during their most controversial campaign speeches and debates for the 2016 United States presidential election. Our facial detection application is based on the Face API recently developed by Microsoft Cognitive Services, which is designed to recognize eight universal groups of facial emotions including sadness, neutral, contempt, disgust, anger, surprise, fear and happiness. 180 images were collected and analyzed for Donald Trump, John Kasich and Ted Cruz; Republican party nominees, also Hillary Clinton and Bernie Sanders for the Democratic party nominees, the results of the detected groups of facial emotions are scored forming an eight-dimensional vector and then re-scaled to two-dimensional vectors using Principal Component Analysis technique, the findings are discussed in the context of direct correlation between some facial expressions and voters decisions for the primary presidential election taking place since February first 2016.

Abstract: A combined approach to identify emotionally colored texts, which reflect the excited state of its authors and also make the sentiment analysis of these texts is proposed. This approach is based on one side on use of psycholinguistic markers that are calculated on the basis of the morphological characteristics of the text and on other side on use of object oriented sentiment analyser based on SVM classification. A complex indicator reflecting emotiveness of texts on the basis of the core group of markers was presented. On an example of two thematic collections it was shown that on the basis of that complex indicator the most emotional topic could be automatically detected. In this article an integrated approach is presented which combines the assessment of the text using the sentiment analysis method and context-independent psycholinguistic markers based on morphological features. The proposed approach can be a useful extension of Social Mining methods in different languages and it can be applicable in developing methods in the fields of affective and personality computing.

Abstract: As Ireland emerges from recession, riding a wave of growth largely driven by the presence of large profitable foreign multi-nationals, recurring questions surrounding the long-term durability of the so-called 'industrialisation by invitation' approach to modernisation persist. If Ireland is to benefit from this strategy, there needs to be significant transfer of knowledge between foreign and domestic firms, thus enabling the latter to emerge as global competitors in their own right. In order to investigate patterns of knowledge diffusion within the Irish economy, here we build a network of labour transitions (job switches) between foreign-owned multi-nationals and domestic firms using a new dataset constructed from the Irish economic census of 2014. Using network techniques for community detection, we identify a highly modular network structure, as workers tend to switch to a narrow set of similar industries that share their own skill set. We find that while some sectors such as pharmaceuticals, with a high share of foreign firms, are largely disconnected from the wider economy, other sectors such as financial services, IT and food processing are more integrated with domestic economic activities. This analysis suggests that policies focusing on increasing labour mobility between certain sectors, and hence enabling workers to move more freely throughout the economy, could result in improved knowledge and expertise transfer from foreign to domestic firms (and vice versa).

Abstract: Technology is a complex system that evolves through the collective efforts of individual inventors. Understanding inventors' behaviors may thus enable predicting invention or improving technology policy. We examined data from 2.8 million inventors' 4 million patents and found most patents are created by ``explorers": inventors who move across different technology domains during their careers. Explorers are far more likely to enter technology domains that were highly related to their own individual inventive experience; this information enabled accurate prediction of individual explorers' future movements. Inventors who entered very related domains patented more there, but explorers who successfully entered moderately related domains were more likely to create high-impact patents. These findings may be instructive for inventors exploring the space of technologies, and useful for organizations or governments in forecasting or directing technological change.

Abstract: We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK, and the US, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent γ ≈ 3 and (ii) an average growing slowly as a power law with an exponent less than one that depends on the country considered. The classical theory for job search is based on the idea that workers evaluate the wage of potential jobs as they arrive sequentially through time, and extending this model with space, we obtain predictions that are strongly contradicted by our empirical findings. We propose an alternative model that is based on the idea that workers evaluate potential jobs based on a quality aspect and that workers search for jobs sequentially across space. We also assume that the density of potential jobs depends on the skills of the worker and decreases with the wage. The predicted distribution of commuting distances decays as 1/r^3 and is independent of the distribution of the quality of jobs. We find our alternative model to be in agreement with our data. This type of approach opens new perspectives for the modeling of mobility.

Abstract: The well-known "Wisdom-of-Crowds" phenomenon, often mistakenly confused with collective intelligence, is not effective in every situation, especially under social influence. In simple estimation tasks, information sharing among group members may lead to strong biases in the collective estimate due to the reduction in diversity and independence of opinions. We are interested in finding conditions where social interactions could improve the accuracy of the collective estimate and its effectiveness. Specifying such conditions is an important step toward understanding how a human group can develop a form of collective intelligence emerging from social interactions between its members. We conduct a series of experiments aiming at understanding how a human group can use social information to converge toward the correct value in an estimation task. Subjects are sequentially asked to give a first guess, and then a second guess in the same estimation task after being provided with information about the average guess of the t previous subjects. We measure how this information affects the initial guesses of the subjects (with weight s) to various questions. We also measure the influence of "experts" (more knowledgeable subjects, introduced artificially with varying probability) and information lifetime (associated to t) on the convergence process. The distribution of social influence s is a Gaussian centered around s=2/3, with two additional very narrow peaks at 0 (highly confident subjects) and 1 ("followers"). We also find values of s below 0 or above 1, which correspond to subjects considered as "irrational" in micro-economic theories, and that may deeply affect the ability of a group to reach the right estimate. Unsurprisingly, the presence of experts improves both the final estimate and the speed of convergence. However, a decrease of the information lifetime t does not seem to influence the accuracy of the final estimate, but noticeably reduces the convergence time.

Abstract: We study the problem of event detection on distributed sensor networks. Prompt event detection is critical for many high-risk settings, for example evacuation following an earthquake. Distributed sensor networks are well suited for this task as they offer advantages such as high reliability and broad coverage. Distributed sensor networks can be organized in a centralized or decentralized way, the former offers higher accuracy, the latter lower communication volume. We study how this tradeoff varies for different network organizations, when a privacy cost is associated with communication. We assume that sensors pay a privacy cost for transmitting measurements. A real world example where this assumptions hold is earthquake detection with smartphones: If a device had to communicate regularly, the receiver could track its position throughout the day. We compare a centralized and a decentralized organization. In the centralized setting all sensors have to send their readings to the central event detection algorithm. In the decentralized setting the algorithm runs locally on a sensor, which alarms the central unit only if detects an event. This setting reduces the communication volume at the expense of accuracy. We propose a distributed protocol that reduces the privacy cost by reducing the communication to the central unit. Reducing communication is by itself desirable whenever remote communication is costly, for example low-power transmitters, and whenever computation is costly, for example if the central unit is a human supervisor with a limited attention span. The protocol allows sensors to ask their neighbors for an opinion on their measurements before reporting an event. The number of neighbors drives the accuracy/communication tradeoff. We test this protocol on different network topologies. We evaluate the system on detection accuracy and privacy cost. We expect to find a range of parameters for which a decentralized organization outperforms a centralized organization.

Abstract: People are constantly moving within cities and countries, facing the fact of the integration in habits and laws of new local cultures. Immigration phenomena have been studied and described so far by census data, which are indeed expensive to take, both in term of cost and time. Here we introduce a new methodology to explore the spatial integration of international immigrant communities in cities, exploring how Twitter users’ language might be a direct connection to their hometown and/or their nationality. We collect Twitter geo-localised data from 2012 to 2015 over a set of 58 out of the most populated cities in the world. We filter the users supposed to be residents in each city and their supposed-to-be place of residency. Finally, we assign to each user its most likely language. We conduct an extensive analysis on users’ spatial distribution within urban areas through a modified entropy metric, as a quantitative measure of the spatial integration of each language in the city. Results allowed us to characterized cities by their "Power of Integration”, as an attitude of hosting immigrant communities in urban areas, and by the corresponding process of integration of languages into different cultures, which is a quantitative measure of the differences between welcoming and hosting people in urban areas. Our findings provide a new way to detect the patterns of historically permanent immigration of people in urban areas, going beyond the estimation of past, current and foreshadowed global flows, towards a better comprehension of spatial integration phenomena on a city scale.

Abstract: Network models of language have provided a way of linking cognitive processes to the structure and connectivity of language. This has been of particular importance in language acquisition as a means to explore the relational role of language and its influence on cognitive processes. Steyvers and Tenenbaum proposed that language is learned by a process similar to preferential attachment, with highly connected nodes being learned earliest, accounting for high-level lexical network structure and also capturing the empirical age of acquisition reports. Hills and colleagues suggested, instead, that language learning is driven by contextual diversity, or the degree of unknown words in the adult language graph, accounting for and predicting normative acquisition trends. Here we extend and test these previous ideas on acquisition trajectories of individual children as opposed to normative acquisition. We further explore the types of relationships between words that are meaningful to toddlers when learning new words. We construct not only theoretical models of acquisition but models that are capable of predicting what words a specific child is likely to learn next. We find that the best fitting network model varies systematically across children and across the course of development. We also find that the choice of network representation influences our ability to model the acquisition trends of young children. This work suggests that the use of network models to understand language acquisition trends of toddlers may not only provide predictive models of what words a child is likely to learn next but may provide insight into the cognitive processes of acquisition itself.

Abstract: Interdisciplinary scientific teams are increasingly funded, but how is knowledge co-produced, in practice, across various disciplines? This paper presents results from a three-year study using a complex systems approach to track the emergence of interdisciplinary science in a heterogeneous researchers network – a “Coupled Human and Natural Systems” research team. I conceptualize the research team as a heterogeneous social network, and analyze the process of knowledge co-production as emergent from the properties and dynamics of the network. The case study is based on epistemological data collected weekly, over three years, from team members (anthropologists, geographers, ecologists, hydrologists, climate scientists and computer scientists) after joint meetings, combined with individual interviews and thematic analyses of research outputs (e.g. articles). I argue that a complex system framework is useful to supports the assessment of what fosters or blocks the emergence of joint knowledge for successful collaborative science.

Abstract: By using a huge Japanese blog data base with the author’s ID, we can observe not only the number of entries per day for any words, but also personal dynamics of blog entries. In this presentation, we report statistical properties and modeling for four major categories of words. The First is “ordinary words” which is used in our daily life, for example “soon”. The number of entries of “soon” has a steady fluctuation. The Second is “News words”, for example “Michael Jackson”. We can observe clear jump and power law decaying in the number of entries of “Michael Jackson” after the news of which Michel Jackson died. The Third is “Trending words”, for example “Twitter”. The number of entries of “Twitter” was increasing exponential from Oct. 2008 to Jun. The fourth is "event words" which has growth and relaxation characterized by a power function around the peak day such as national holidays. We reproduced these dynamics by an agent-based model based on the SIR model which is well known in mathematical epidemiology to clarify the origin of these dynamics from the view point of bloggers interactions. In order to reproduce not only an exponential but also a power law growth and relaxation behaviors observed in trending words, we developed the base model by adding some effects to our model, for example an external shock effect, a deadline effect and an amorphous effect. The amorphous effect, inspired by solid physics studies, gives bloggers individual characteristics, in other words individual duration of interest for the specific word. As a result of adding these essential effects, our model reasonably reproduces the dynamics observed from our data.

Abstract: This presentation argues that crises are a distinctive feature of complex social systems. A quest for connectivity of communication leads to increase systems’ own robustness by constantly producing further connections. When some of these connections have been successful in recent operations, the social system tends to reproduce the emergent pattern, thereby engaging in a non-reflexive, repetitive escalation of more of the same communication. This compulsive growth of systemic communication in crisis processes, or logic of excess, resembles the dynamic of self-organized criticality. Our theoretical model contend that crises in complex social systems are not a singular event, but result from a process that unfolds in three stages: incubation, in which the system incrementally develops a recursive dynamics of non-reflexive repetitions that weakens both its adaptive capabilities and connections; contagion, whereby the effects of that dynamics expands to different systems or clusters in the network; and restructuring, namely, a reorganization of both the system’s own conditions of functioning and its interrelationships with the environment. Next, we argue that percolation and sand pile models are suitable techniques for both modeling this process and analytically distinguishing between three phases of social crises. We illustrate our propositions with a view on the crisis of the educational system in Chile—a country in which over the last forty neoliberal reforms led to an incremental monetization of public education. Accordingly, we first construct the conceptual foundations of our approach. Second, we present three core assumptions related to the generative mechanism of social crises, their temporal transitions (incubation, contagion, restructuring), and the suitable modeling techniques to represent them. Third, we illustrate the conceptual approach with a percolation model of the crisis in Chilean education system.

Abstract: According to psycholinguistics, the human mind organises words in a mental lexicon (ML), i.e. a dictionary where words are stored and retrieved depending on their correlations. Until recently, network theory has been used for investigating one type of interactions at a time, without providing cross-correlational information. Our novel approach overcomes this limitation by modelling the mental lexicon of English speakers as a multiplex lexicon network (MLN), where nodes/words are connected according to: (i) word associations (“A” makes one think of “B”), (ii) feature norms (“A” shares features with “B”), (iii) co-occurrences (“A” and “B” are frequently adjacent), (iv) synonyms ("A" means also "B") and (v) phonological similarities (“A” differs from “B” by the addition, deletion or substitution of one phoneme). We build two MLNs: one for children up to 32 months (with 529 words) and one for adults (with almost 5000 words). Both the MLNs are irreducible, i.e. projecting all the edges onto one aggregate layer only would imply losing information about the word patterns in the system. In children, we show that the multiplex topology is more powerful in predicting the ordering with which words are acquired than individual layer statistics. Also, multiplexity allows for a quantification of the most important layers (semantic vs. phonological) that dynamically determine word acquisition. For adults, we propose a novel toy model of lexicon growth driven by the phonological level, in which real words are inserted along different orderings and they can be also rejected for memorization. Our model shows that when similar-sounding words are preferentially learned, the lexicon grows according to the multiplex structure, while when novel learned words sound different from the known ones, both semantic layers and frequency become predominant, instead. Our results indicate that the MLN topology is a meaningful proxy of the cognitive processes shaping the mental lexicon.

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.