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Introduction The power-law distribution is common in the nature world and our social life. In the field of Information Science, the Lotka's Law, which describes the scientific productivity, and the Zipf's Law, which describes

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taggers and IO professionals. Up until now, three different approaches have been adopted to study the use of social tags in the IO domain. Several studies have examined whether use of social tags generally follows a power-law distribution (Angus et al

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In a one-parameter model for evolution of random trees strong law of large numbers and central limit theorem are proved for the number of vertices with low degree. The proof is based on elementary martingale theory.

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Abstract

While there is a consensus that there is a core-periphery structure in the global scientific enterprise, there have not been many methodologies developed for identifying this structure. This paper develops a methodology by looking at the differences in the power law structure of article outputs and degree centrality distributions of countries. This methodology is applied to five different scientific fields: astronomy and astrophysics, energy and fuels, nanotechnology and nanosciences, nutrition, and oceanography. This methodology uncovers a two-tiered power law structure that exists in all examined fields. The core-periphery structure that is unique to each field is characterized by the core's size, minimum degree, and exponent of its power law distribution. Stark differences are identified between technology and non-technology intensive scientific fields.

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): A Theory of Power-law Distributions in Financial Market Fluctuations. Nature 423: 267–270. Stanley H. E. A Theory of Power-law Distributions in Financial Market Fluctuations

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distribution, but on a log–log scale. This distribution appears to be nearly linear. This is the characteristic signature of a power-law distribution. It is reported that most of the real-world networks including the World Wide Web (Huberman and Adamic 1999

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Gabaix, X., Gopikrishan, P., Plerou, V., Stanley, H. E. (2003): A Theory of Power-law Distributions in Financial Market Fluctuations. Nature 423 : 267-270. A Theory of Power-law Distributions in Financial Market Fluctuations

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. , LOTKA: A program to fit a power law distribution to observed frequency data . Cybermetrics , 4 ( 1 ) ( 2000 ). Available at http://www.cindoc.csic.es/cybermetrics/articles/v4ilp4.html . 25

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research on the concept of complex network to new heights. Citation networks possess the characteristics of complex networks, and they have a power law distribution with an index of about 3 (Redner 1998 ). As an effective approach to catch the features of

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. Milojević , S 2010 Power-law distributions in information science—Making the case for logarithmic binning . Journal of the American Society for Information Science and Technology 61 12 2417 – 2425 10.1002/asi.21426

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