Impact in informetrics and beyond
Leo Egghe, Ronald Rousseau

TL;DR
This paper develops a mathematical framework for measuring impact in informetrics, analyzing various impact measures, bundles, and the Lorenz order to quantify influence of sources like authors or journals.
Contribution
It introduces a formal, multi-level mathematical approach to defining and comparing impact measures, including impact bundles and Lorenz order-based impact.
Findings
Impact measures based on rank-frequency functions are formalized.
Impact bundles provide a more comprehensive impact assessment.
Non-normalized Lorenz order offers a rigorous way to compare impact levels.
Abstract
The concept of impact is one of the most important concepts in informetrics. It is here studied mathematically. We first fix a topic for which we want to find influential objects such as authors or journals, and their production, such as publications generating citations. These objects are then said to have a certain degree of impact. We work on three levels. On the first level, we need a measure for these objects, represented by their rank-frequency function, describing the number of items per source (ranked in decreasing order of the number of items): an impact measure. These measures focus on the production of the most productive sources. The h-index is one example. In paper II we study a formal definition of impact measures based on these left-hand sides of the source-item rank-frequency functions representing these objects. The second level of impact investigation is using impact…
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Taxonomy
TopicsComplex Systems and Time Series Analysis
