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The Pinski–Narin influence weight and the Ramanujacharyulu power-weakness ratio indicators revisited

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  • Gangan Prathap

    (A P J Abdul Kalam Technological University)

Abstract

A graph theoretic approach from social network analysis allows size-dependent and size-independent bibliometric indicators to be identified from what is called the citation matrix. In an input–output sense, the number of references becomes the size-dependent measure of the input and the number of citations received by the journal from all journals in the network becomes the size-dependent measure of the output. However, in this paper, we are interested to compare two size-independent dimensionless indicators: the Pinski–Narin influence weight (IW) and the Ramanujacharyulu power-weakness ratio (PWR). These are proxies for the quality of the journal’s performance in the network. We show that at the non-recursive level, the two indicators are identical. At this stage these are simply measures of popularity. After recursion (i.e. repeated improvement or iteration) these become network measures of prestige of the journals. PWR is computed as a ratio of terms in the weighted citations vector and weighted references vector after the power and weakness matrices are separately recursively iterated. The Pinski–Narin procedure computes a matrix of ratios first and evaluates the IW after recursive iteration of this matrix of ratios. In this sense, the two procedures differ just like the RoA (ratio of averages) and the AoR (average of ratios) ways of computing relative citation indicators. We illustrate the concepts using datasets from subgraphs of 10 statistical journals and 14 Chinese chemistry journals with network data collected from the Web of Science. We are also able to show the confounding effects when self-citations are taken into account.

Suggested Citation

  • Gangan Prathap, 2019. "The Pinski–Narin influence weight and the Ramanujacharyulu power-weakness ratio indicators revisited," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(2), pages 1173-1185, May.
    • Handle: RePEc:spr:scient:v:119:y:2019:i:2:d:10.1007_s11192-019-03046-7
    DOI: 10.1007/s11192-019-03046-7
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    References listed on IDEAS

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    1. Gangan Prathap, 2018. "Eugene Garfield: from the metrics of science to the science of metrics," Scientometrics, Springer;Akadémiai Kiadó, vol. 114(2), pages 637-650, February.
    2. Johan Bollen & Herbert Van de Sompel & Aric Hagberg & Ryan Chute, 2009. "A Principal Component Analysis of 39 Scientific Impact Measures," PLOS ONE, Public Library of Science, vol. 4(6), pages 1-11, June.
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    7. Erjia Yan & Ying Ding, 2010. "Weighted citation: An indicator of an article's prestige," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 61(8), pages 1635-1643, August.
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    Cited by:

    1. Prathap, Gangan & Mukherjee, Somenath & Leydesdorff, Loet, 2020. "Within-journal self-citations and the Pinski-Narin influence weights," Journal of Informetrics, Elsevier, vol. 14(1).
    2. Ephrance Abu Ujum & Sameer Kumar & Kuru Ratnavelu & Gangan Prathap, 2021. "A new journal power-weakness ratio to measure journal impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9051-9068, November.

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