## Abstract

Applying the concept of triadic closure to coauthorship networks means that scholars are likely to publish a joint paper if they have previously coauthored with the same people. Prior research has identified moderate to high (20 to 40%) closure rates; suggesting this mechanism is a reasonable explanation for tie formation between future coauthors. We show how calculating triadic closure based on prior operationalizations of closure, namely Newman’s measure for one-mode networks (NCC) and Opsahl’s measure for two-mode networks (OCC) may lead to higher amounts of closure compared to measuring closure over time via a metric that we introduce and test in this paper. Based on empirical experiments using four large-scale, longitudinal datasets, we find a lower bound of 1–3% closure rates and an upper bound of 4–7%. These results motivate research on new explanatory factors for the formation of coauthorship links.

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## Notes

- 1.
- 2.
The triadic closure contains three cases of 2-path closure: (1) Y–X–Z closed by Y–Z, (2) X–Z–Y closed by Y–X, and (3) Z–Y–X closed by X–Z. This also applies to Case 2 in Table 2.

- 3.
The triadic closure contains three cases of 4-path closure: (1) Y–A–X–B–Z closed by Y–C–Z, (2) X–B–Z–C–Y closed by Y–A–X, and (3) Z–C–Y–A–X closed by X–B–Z.

- 4.
- 5.
Opsahl (2013) never uses the clustering coefficient defined for two-mode networks as an indicator of the probability of two scientists collaborating when they have a third coauthor in common.

- 6.
- 7.
The list of 392 journals was obtained from Thomson Reuters Journal Citation Report 2012 for the Computer Science category. Then, those journals’ names and papers published in these journals were searched for in DBLP.

- 8.
- 9.
- 10.
- 11.
The 4-path in Case 1 is Y–A–X–B–Z. The 4-paths in Case 2 are: (1) Y–A–X–B–Z, (2) Y–A–W–B–Z, and (3) Y–C–X–B–Z.

- 12.
In 2010, OCC (0.34) surpasses NCC (0.33).

- 13.
4-paths by OCC: (1) Y–B–X–C–Z (closed by Z–D–Y), (2) Y–A–X–C–Z (closed by Z–D–Y), (3) X–C–Z–D–Y (closed by Y–A–X or Y–B–X), (4) Z–D–Y–A–X (closed by X–C–Z), (5) Z–D–Y–B–X (closed by X–C–Z), (6) X–C–Z–E–W, and (7) W–E–Z–D–Y.

- 14.
2-paths by NCC: (1) Y–X–Z (Y–Z), (2) X–Z–Y (Y–Z), (3) Z–Y–X (X–Z), (4) W–Z–X, and (5) W–Z–Y.

- 15.
4-paths by TCC: (1) Y–A and B–X–C–Z (closed by Z–D–Y) and (2) X–C–Z–E–W.

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## Acknowledgements

This work was supported by Korea Institute of Science and Technology Information (KISTI). We would like to thank Mark E. J. Newman and Tore Opsahl for providing codes.

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Kim, J., Diesner, J. Over-time measurement of triadic closure in coauthorship networks.
*Soc. Netw. Anal. Min.* **7, **9 (2017). https://doi.org/10.1007/s13278-017-0428-3

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### Keywords

- Clustering coefficient
- Transitivity
- Triadic closure
- Coauthorship networks