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The Power-weakness Ratios (PWR) as a Journal Indicator: Testing the “Tournaments” Metaphor in Citation Impact Studies

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Ramanujacharyulu developed the Power-weakness Ratio (PWR) for scoring tournaments. The PWR algorithm has been advocated (and used) for measuring the impact of journals. We show how such a newly proposed indicator can empirically be tested.


PWR values can be found by recursively multiplying the citation matrix by itself until convergence is reached in both the cited and citing dimensions; the quotient of these two values is defined as PWR. We study the effectiveness of PWR using journal ecosystems drawn from the Library and Information Science (LIS) set of the Web of Science (83 journals) as an example. Pajek is used to compute PWRs for the full set, and Excel for the computation in the case of the two smaller sub-graphs: (1) JASIST+ the seven journals that cite JASIST more than 100 times in 2012; and (2) MIS Quart+ the nine journals citing this journal to the same extent.


A test using the set of 83 journals converged, but did not provide interpretable results. Further decomposition of this set into homogeneous sub-graphs shows that—like most other journal indicators—PWR can perhaps be used within homogeneous sets, but not across citation communities. We conclude that PWR does not work as a journal impact indicator; journal impact, for example, is not a tournament.

Research limitations

Journals that are not represented on the “citing” dimension of the matrix-for example, because they no longer appear, but are still registered as “cited” (e.g. ARIST)-distort the PWR ranking because of zeros or very low values in the denominator.

Practical implications

The association of “cited” with “power” and “citing” with “weakness” can be considered as a metaphor. In our opinion, referencing is an actor category and can be studied in terms of behavior, whereas “citedness” is a property of a document with an expected dynamics very different from that of “citing.” From this perspective, the PWR model is not valid as a journal indicator.


Arguments for using PWR are: (1) its symmetrical handling of the rows and columns in the asymmetrical citation matrix, (2) its recursive algorithm, and (3) its mathematical elegance. In this study, PWR is discussed and critically assessed.