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Abstract

Measurement of the degree of interconnectedness in graph like networks of hyperlinks or citations can indicate the existence of research fields and assist in comparative evaluation of research efforts. In this issue we begin with Egghe and Rousseau who review compactness measures and investigate the compactness of a network as a weighted graph with dissimilarity values characterizing the arcs between nodes. They make use of a generalization of the Botofogo, Rivlin, Shneiderman, (BRS) compaction measure which treats the distance between unreachable nodes not as infinity but rather as the number of nodes in the network. The dissimilarity values are determined by summing the reciprocals of the weights of the arcs in the shortest chain between two nodes where no weight is smaller than one. The BRS measure is then the maximum value for the sum of the dissimilarity measures less the actual sum divided by the difference between the maximum and minimum. The Wiener index, the sum of all elements in the dissimilarity matrix divided by two, is then computed for Small's particle physics co-citation data as well as the BRS measure, the dissimilarity values and shortest paths. The compactness measure for the weighted network is smaller than for the un-weighted. When the bibliographic coupling network is utilized it is shown to be less compact than the co-citation network which indicates that the new measure produces results that confirm to an obvious case.

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Date

14. 2.2012 12:53:22

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Abstract

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 seif-similarity property) as weIl 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 seif-similar fractal and show the relation between Lotka's exponent and the (seif-similar) fractal dimension of the system. Lotkaian informetric systems are seif-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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Source

Journal of information science. 22(1996) no.3, S.165-170

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Date

14. 8.2004 19:17:22