We study the evolution of long-lived controversial debates as manifested on Twitter from 2011 to 2016. Specifically, we explore how the structure of interactions and content of discussion varies with the level of collective attention, as evidenced by the number of users discussing a topic. Spikes in the volume of users typically correspond to external events that increase the public attention on the topic -- as, for instance, discussions about gun control' often erupt after a mass shooting. This work is the first to study the dynamic evolution of polarized online debates at such scale. By employing a wide array of network and content analysis measures, we find consistent evidence that increased collective attention is associated with increased network polarization and network concentration within each side of the debate; and overall more uniform lexicon usage across all users.
Social networking services are a fast-growing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in real-life social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, each with more than 10 million users, respectively. We have access to complete data of Cyworld's ilchon (friend) relationships and analyze its degree distribution, clustering property, degree correlation, and evolution over time. We also use Cyworld data to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace and orkut. Cyworld, the oldest of the three, demonstrates a changing scaling behavior over time in degree distribution. The latest Cyworld data's degree distribution exhibits a multi-scaling behavior, while those of MySpace and orkut have simple scaling behaviors with different exponents. Very interestingly, each of the two e ponents corresponds to the different segments in Cyworld's degree distribution. Certain online social networking services encourage online activities that cannot be easily copied in real life; we show that they deviate from close-knit online social networks which show a similar degree correlation pattern to real-life social networks. How do real graphs evolve over time? What are "normal" growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time.Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)).Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a "forest fire" spreading process, that has a simple, intuitive justification, requires very few parameters (like the "flammability" of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. We present a detailed study of network evolution by analyzing four large online social networks with full temporal information about node and edge arrivals. For the first time at such a large scale, we study individual node arrival and edge creation processes that collectively lead to macroscopic properties of networks. Using a methodology based on the maximum-likelihood principle, we investigate a wide variety of network formation strategies, and show that edge locality plays a critical role in evolution of networks. Our findings supplement earlier network models based on the inherently non-local preferential attachment. Based on our observations, we develop a complete model of network evolution, where nodes arrive at a prespecified rate and select their lifetimes. Each node then independently initiates edges according to a "gap" process, selecting a destination for each edge according to a simple triangle-closing model free of any parameters. We show analytically that the combination of the gap distribution with the node lifetime leads to a power law out-degree distribution that accurately reflects the true network in all four cases. Finally, we give model parameter settings that allow automatic evolution and generation of realistic synthetic networks of arbitrary scale.