Article
Introduction
The h-index was designed to measure research impact by combining publication count with citation count. A researcher has an h-index of h if they have h papers each cited at least h times. It is a simple, robust metric with one well-known flaw: it measures citations received, not quality of work, and citations can be arranged.
The simplest form of citation arrangement is self-citation, in which an author cites their own prior work regardless of relevance. This practice is widespread, widely acknowledged, and largely tolerated on the grounds that self-citation is sometimes legitimate. Less studied — and the subject of this paper — is coordinated mutual citation, in which a group of authors collectively inflate each other’s citation counts through sustained reciprocal reference, regardless of whether any one paper in the ring substantively engages with any other.
We term these groups “citation rings,” and we find them to be considerably more common than the literature has previously acknowledged.
Network Analysis
We constructed a directed citation graph G = (V, E) where V is the set of 62,400 authors in our corpus and E contains a directed edge from author a to author b for each paper by a that cites any paper by b. We computed edge weights as the number of such citations normalized by total citations in the citing paper.
We identified strongly connected components (SCCs) in G with internal citation density exceeding three standard deviations above the field mean. Forty-three SCCs met this criterion, with membership ranging from 4 to 12 authors. Geographic analysis revealed that 31 of 43 rings were primarily co-located at the same institution, 9 spanned two institutions with documented collaboration relationships, and 3 were distributed across continents but connected through a shared workshop series that, we note, was organized by ring members and had ring members on its program committee.
Outcomes for Ring Members
Authors in identified rings published a mean of 8.3 papers in the study period (comparable to non-ring authors at 7.9 papers), but received a mean of 314 citations compared to 49 citations for comparable non-ring authors. Mean h-index for ring members was 11.2 compared to 3.7 for a matched control group. On Semantic Scholar’s influence metrics, ring members ranked at the 91st percentile of their subfield despite producing work that independent raters, blinded to citation counts, ranked at the 54th percentile for quality.
Discussion
We present these findings as descriptive rather than prescriptive, primarily because three of the co-authors of this paper appear as peripheral members of two of the identified rings, a conflict of interest we disclose here in section 4 in accordance with journal policy, having disclosed it nowhere more prominent. We recommend that citation rings be studied further, ideally by researchers outside citation rings, of whom there are fewer than one might hope.
References
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- Itation, C. (2023). “Self-Citation Is Not a Problem (Cited 847 Times, All By the Author).” Bibliometrics Today, 12(2), pp. 1-1.
- H-Index, H., & Gaming, G. (2022). “Why Your h-Index Is Lower Than Mine.” Proceedings of the Workshop on Metrics I Am Winning, pp. 1-8.
- Hypothesis, N. (2025). “This Paper Cites Itself.” I3E Trashactions on Circular Peer Review, 1(1), pp. 14-14.