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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/9281

Title: Lotkaian informetrics and applications to social networks
Authors: EGGHE, Leo
Issue Date: 2009
Publisher: BELGIAN MATHEMATICAL SOC TRIOMPHE, CP 218,01 BOULEVARD TRIOMPE, B 1050 BRUSSELS, BELGIUM
Citation: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 16(4). p. 689-703
Abstract: Two-dimensional informetrics is defined in the general context of sources that produce items and examples are given. These systems are called "Information Production Processes" (IPPs). They can be described by a size-frequency function f or, equivalently, by a rank-frequency function g. If f is a decreasing power law then we say that this function is the law of Lotka and it is equivalent with the power law g which is called the law of Zipf. Examples in WWW are given. Next we discuss the scale-free property of f also allowing for the interpretation of a Lotkaian IPP (i.e. for which f is the law of Lotka) as a self-similar fractal. Then we discus-dynamical aspects of (Lotkaian) IPPs by introducing an item-transformation phi and a source-transformation psi. If these transformations are power functions we prove that the transformed IPP is Lotkaian and we present a formula for the exponent of the Lotka law. Applications are given on the evolution of WWW and on IPPs without low productive sources (e.g. sizes of countries, municipalities or databases). Lotka's law is then used to model the cumulative first citation distribution and examples of good fit are given. Finally, Lotka's law is applied to the study of performance indices such as the h-index (Hirsch) or the g-index (Egghe). Formulas are given for the hand g-index in Lotkaian IPPs and applications are given.
URI: http://hdl.handle.net/1942/9281
ISI #: 000272832300008
ISSN: 1370-1444
Category: A1
Type: Journal Contribution
Validation: ecoom, 2010
Appears in Collections: Research publications

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