Bradford's Law of Bibliography of Science: an Interpretation

Naranan, S.

doi:10.1038/227631a0

Cited by 63 publications

(43 citation statements)

References 3 publications

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“…The importance lies in the fact that power laws (and only power laws) satisfy the so-called scale-free property, which makes systems self-similar at any measuring scale. This conclusion leads to the concept of self-similar fractals and an old argument of Naranan (1970). His idea for continuous time is extended here so that it is also valid in discrete time.…”

Section: Discussionmentioning

confidence: 88%

“…In the next section, Naranan's argument leading to a power law for the sizefrequency function f is presented and a formula for Lotka's exponent a in function of both growth rates is deduced. This is also done in Naranan (1970) but the fractal argument, based on this formula is missing there; it is given here in the Complexity in Informetrics section, thus showing the full importance of Naranan's work. In the Discrete Time Argument section, we will present a discrete-time variant of the argument of Naranan that is presented in the next section, leading to the same law of Lotka.…”

Section: Proof Of Lotka's Law Based On Exponential Growthmentioning

confidence: 95%

“…Then, an old argument of Naranan (1970) is reproduced, showing that Lotka's law can be derived from the exponential growth of the number of articles in a journal and the exponential growth of the number of journals. Also a discretetime argument is given, yielding again the same law of Lotka.…”

Section: Introductionmentioning

confidence: 99%

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The power of power laws and an interpretation of Lotkaian informetric systems as self‐similar fractals

Egghe

2005

J. Am. Soc. Inf. Sci.

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Power laws as defined in 1926 by A. Lotka are increasing in importance because they have been found valid in varied social networks including the Internet. In this article some unique properties of power laws are proven. They are shown to characterize functions with the scalefree property (also called self-similarity property) as well as functions with the product property. Power laws have other desirable properties that are not shared by exponential laws, as we indicate in this paper. Specifically, Naranan (1970) proves the validity of Lotka's law based on the exponential growth of articles in journals and of the number of journals. His argument is reproduced here and a discrete-time argument is also given, yielding the same law as that of Lotka. This argument makes it possible to interpret the information production process as a self-similar fractal and show the relation between Lotka's exponent and the (self-similar) fractal dimension of the system. Lotkaian informetric systems are self-similar fractals, a fact revealed by Mandelbrot (1977) in relation to nature, but is also true for random texts, which exemplify a very special type of informetric system.

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Section: Discussionmentioning

confidence: 88%

Section: Proof Of Lotka's Law Based On Exponential Growthmentioning

confidence: 95%

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The power of power laws and an interpretation of Lotkaian informetric systems as self‐similar fractals

Egghe

2005

J. Am. Soc. Inf. Sci.

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“…However, the phenomena of obsolescence and growth of quotations on a subject of search in scientific literature (Egghe, 1993) are modeled by exponential processes. In addition, the often ignored result of Naranan (Naranan, 1971), shows that distributions of Lotkaian type can be deduced under certain conditions from an exponential growth of sources and the number of items produced by these sources. It gives the exponential functions an importance that we cannot neglect.…”

Section: Lotkaian Informetric Distributionmentioning

confidence: 99%

The source-item coverage of the exponential function

Lafouge

2007

Journal of Informetrics

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Statistical distributions in the production of information are most often studied in the framework of Lotkaian informetrics. In this article, we recall some results of basic theory of Lotkaian informetrics, then we transpose methods (Theorem1) applied to Lotkaian distributions by Leo Egghe (Theorem 2) to the exponential distributions (Theorem 3, Theorem 4). We give examples and compare the results (Theorem 5). Finally, we propose to widen the problem using the concept of exponential informetric process (Theorem 6).

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“…We have to conclude that either the bibliography or database used by Nweke has some peculiar feature or the methodology followed for estimation is not good. (Naranan, 1970) 6 in his explanation of Bradford's law assumed a time dependent exponential growth of both sources and items. His final result is a power law independent of time and devoid of any real predictive power (by predictive power we mean either of forecasting or of estimation as already discussed).…”

Section: Introductionmentioning

confidence: 99%

Bibliographic scattering and time: An empirical study through temporal partitioning of bibliographies

Sen

Chatterjee

1998

Scientometrics

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Time dependence of bibliographic scattering is not at all understood. There are not many studies to establish any relation between growth of a bibliography over time and scattering. In this empirical study three different types of bibliographies have been taken. Each bibliography has been partitioned in different temporal periods (according as the particular bibliography should allow). The complete bibliography and the partitions have then been used to draw corresponding Bradford bibliographs whose natures have been studied. No conclusive relation between growth and scattering could be drawn except that the nature of the bibliograph depends on the value of concentration that is the ratio of the number of items and the number of sources in the bibliography. The paper shows that much needs to be done in this area and partition studies may be a useful technique.

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Bradford's Law of Bibliography of Science: an Interpretation

Cited by 63 publications

References 3 publications

The power of power laws and an interpretation of Lotkaian informetric systems as self‐similar fractals

The power of power laws and an interpretation of Lotkaian informetric systems as self‐similar fractals

The source-item coverage of the exponential function

Bibliographic scattering and time: An empirical study through temporal partitioning of bibliographies

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