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      Structural and Dynamical Patterns on Online Social Networks: The Spanish May 15th Movement as a Case Study

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          Abstract

          The number of people using online social networks in their everyday life is continuously growing at a pace never saw before. This new kind of communication has an enormous impact on opinions, cultural trends, information spreading and even in the commercial success of new products. More importantly, social online networks have revealed as a fundamental organizing mechanism in recent country-wide social movements. In this paper, we provide a quantitative analysis of the structural and dynamical patterns emerging from the activity of an online social network around the ongoing May 15th (15M) movement in Spain. Our network is made up by users that exchanged tweets in a time period of one month, which includes the birth and stabilization of the 15M movement. We characterize in depth the growth of such dynamical network and find that it is scale-free with communities at the mesoscale. We also find that its dynamics exhibits typical features of critical systems such as robustness and power-law distributions for several quantities. Remarkably, we report that the patterns characterizing the spreading dynamics are asymmetric, giving rise to a clear distinction between information sources and sinks. Our study represents a first step towards the use of data from online social media to comprehend modern societal dynamics.

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          Epidemic Spreading in Scale-Free Networks

          The Internet has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and persistence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks, finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.
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            Neocortex size as a constraint on group size in primates

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              Scaling laws of human interaction activity.

              Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2011
                19 August 2011
                : 6
                : 8
                : e23883
                Affiliations
                [1 ]Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain
                [2 ]Departamento de Física Teórica, Universidad de Zaragoza, Zaragoza, Spain
                [3 ]Cierzo Development S.L., Zaragoza, Spain
                [4 ]Fundación ARAID, Diputación General de Aragón, Zaragoza, Spain
                [5 ]Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Torino, Italy
                University of Maribor, Slovenia
                Author notes

                Conceived and designed the experiments: JB-H AT YM. Performed the experiments: JB-H AR IG EC AF D. Ferrer D. Francos DI MPP GR F. Sanz F. Serrano CV AT YM. Analyzed the data: JB-H AR AT YM. Contributed reagents/materials/analysis tools: JB-H YM. Wrote the paper: JB-H YM.

                Article
                PONE-D-11-13991
                10.1371/journal.pone.0023883
                3158778
                21886834
                0f6b1438-a5b2-4638-98c6-a325b568c5cf
                Borge-Holthoefer et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                History
                : 8 July 2011
                : 30 July 2011
                Page count
                Pages: 8
                Categories
                Research Article
                Mathematics
                Applied Mathematics
                Nonlinear Dynamics
                Probability Theory
                Stochastic Processes
                Statistics
                Physics
                Interdisciplinary Physics
                Statistical Mechanics
                Social and Behavioral Sciences
                Information Science
                Sociology
                Computational Sociology
                Culture
                Social Mobility
                Social Networks
                Social Systems
                Social Welfare
                Sociometry

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                Uncategorized

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