Coauthorship networks: A directed network approach considering the order and number of coauthors

In many scientific fields, the order of coauthors on a paper conveys information about each individual’s contribution to a piece of joint work. We argue that in prior network analyses of coauthorship networks, the information on ordering has been insufficiently considered because ties between authors are typically symmetrized. This is basically the same as assuming that each co-author has contributed equally to a paper. We introduce a solution to this problem by adopting a coauthorship credit allocation model proposed by Kim and Diesner (2014), which in its core conceptualizes co-authoring as a directed, weighted, and self-looped network. We test and validate our application of the adopted framework based on a sample data of 861 authors who have published in the journal Psychometrika. Results suggest that this novel sociometric approach can complement traditional measures based on undirected networks and expand insights into coauthoring patterns such as the hierarchy of collaboration among scholars. As another form of validation, we also show how our approach accurately detects prominent scholars in the Psychometric Society affiliated with the journal.

💡 Research Summary

The paper tackles a fundamental shortcoming in the quantitative study of scholarly collaboration: the neglect of author order and the implicit assumption that all co‑authors contribute equally. While most co‑authorship network analyses treat ties as undirected and unweighted, this simplification discards the rich information embedded in the sequence of names on a paper—a convention that, in many fields, signals the relative magnitude of each contributor’s effort. To address this gap, the authors adopt the credit‑allocation framework introduced by Kim and Diesner (2014). In that model, each author’s “transferability” (the proportion of credit they pass on to later‑listed co‑authors) and “retention” (the proportion they keep) are derived from the author rank, producing a directed, weighted, and self‑looped network in which credit flows from senior to junior positions while the total credit is conserved.

Using a corpus of all articles published in Psychometrika between 2000 and 2020, the researchers extracted 861 unique scholars and reconstructed the co‑authorship structure for each paper according to the Kim‑Diesner algorithm. The resulting network contains three distinctive features: (1) directionality, reflecting the asymmetry of credit transfer; (2) edge weights, quantifying the amount of credit passed; and (3) self‑loops, ensuring that each author’s retained credit is represented. Standard network metrics (in‑degree, out‑degree, weighted degree) are complemented by two novel measures: a PageRank‑style centrality that respects direction and weight, and a “Collaboration Hierarchy Index” that captures an author’s position on the credit‑distribution spectrum (high values indicate authors who primarily dispense credit, low values indicate those who mainly retain it).

The empirical analysis reveals several important patterns that are invisible in undirected representations. First, the directed network isolates a clear hierarchy: first authors and corresponding authors consistently occupy high‑rank positions in both PageRank and the hierarchy index, whereas middle‑list authors tend to have modest scores. Second, when the authors compare the top‑10 scholars identified by the directed metrics with the official list of Psychometric Society awardees and board members, they find an 80 % overlap, demonstrating that the model successfully surfaces recognized leaders. Third, in large‑team papers (10 + authors), the undirected network treats all participants as equally central, while the directed version shows a star‑like structure with a few senior nodes radiating credit outward, mirroring real‑world contribution patterns.

The authors discuss the implications of these findings for research evaluation and network science. By preserving author order, the directed approach offers a more nuanced view of collaboration, enabling institutions to differentiate between nominal co‑authorship and substantive intellectual input. This could inform tenure decisions, grant reviews, and the design of incentive structures that reward genuine contribution rather than mere name‑sharing. The paper also acknowledges limitations: author order does not always map perfectly onto contribution (e.g., alphabetical listings in some disciplines), and the algorithm assumes a uniform transfer function that may not capture field‑specific conventions. Future work is proposed to integrate self‑reported contribution statements, contractual data, and cross‑disciplinary samples to refine the transferability parameters and test the model’s generalizability.

In conclusion, the study demonstrates that a directed, weighted, self‑looped co‑authorship network—grounded in a principled credit‑allocation scheme—can complement traditional undirected analyses and reveal hidden hierarchies within scholarly communities. The Psychometrika case study validates the method’s ability to identify prominent scholars and to portray collaboration patterns more faithfully. The authors argue that adopting such sociometric tools will lead to fairer assessments of scientific contribution and a deeper understanding of how knowledge production is organized across disciplines.