
arXiv: 1307.8250
A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the system abruptly changes. For example, such critical transitions may result in the sudden change of ecological environments and climate conditions. Data and models suggest that detectable warning signs may precede some of these drastic events. This view is also corroborated by abstract mathematical theory for generic bifurcations in stochastic multi-scale systems. Whether the stochastic scaling laws used as warning signs are also present in social networks that anticipate a-priori {\it unknown} events in society is an exciting open problem, to which at present only highly speculative answers can be given. Here, we instead provide a first step towards tackling this formidable question by focusing on a-priori {\it known} events and analyzing a social network data set with a focus on classical variance and autocorrelation warning signs. Our results thus pertain to one absolutely fundamental question: Can the stochastic warning signs known from other areas also be detected in large-scale social network data? We answer this question affirmatively as we find that several a-priori known events are preceded by variance and autocorrelation growth. Our findings thus clearly establish the necessary starting point to further investigate the relation between abstract mathematical theory and various classes of critical transitions in social networks.
14 pages, 5 figures, revised and extended version
Social and Information Networks (cs.SI), FOS: Computer and information sciences, Physics - Physics and Society, FOS: Physical sciences, Computer Science - Social and Information Networks, Physics and Society (physics.soc-ph), Nonlinear Sciences - Adaptation and Self-Organizing Systems, Physics - Data Analysis, Statistics and Probability, Adaptation and Self-Organizing Systems (nlin.AO), Data Analysis, Statistics and Probability (physics.data-an)
Social and Information Networks (cs.SI), FOS: Computer and information sciences, Physics - Physics and Society, FOS: Physical sciences, Computer Science - Social and Information Networks, Physics and Society (physics.soc-ph), Nonlinear Sciences - Adaptation and Self-Organizing Systems, Physics - Data Analysis, Statistics and Probability, Adaptation and Self-Organizing Systems (nlin.AO), Data Analysis, Statistics and Probability (physics.data-an)
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