Metrics to Detect Small-Scale and Large-Scale Citation Orchestration

Citation counts and related metrics have pervasive uses and misuses in academia and research appraisal, serving as scholarly influence and recognition measures. Hence, comprehending the citation patterns exhibited by authors is essential for assessing their research impact and contributions within their respective fields. Although the h-index, introduced by Hirsch in 2005, has emerged as a popular bibliometric indicator, it fails to account for the intricate relationships between authors and their citation patterns. This limitation becomes particularly relevant in cases where citations are strategically employed to boost the perceived influence of certain individuals or groups, a phenomenon that we term "orchestration". Orchestrated citations can introduce biases in citation rankings and therefore necessitate the identification of such patterns. Here, we use Scopus data to investigate orchestration of citations across all scientific disciplines. Orchestration could be small-scale, when the author him/herself and/or a small number of other authors use citations strategically to boost citation metrics like h-index; or large-scale, where extensive collaborations among many co-authors lead to high h-index for many/all of them. We propose three orchestration indicators: extremely low values in the ratio of citations over the square of the h-index (indicative of small-scale orchestration); extremely small number of authors who can explain at least 50% of an author's total citations (indicative of either small-scale or large-scale orchestration); and extremely large number of co-authors with more than 50 co-authored papers (indicative of large-scale orchestration). The distributions, potential thresholds based on 1% (and 5%) percentiles, and insights from these indicators are explored and put into perspective across science.