Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Over-time measurement of triadic closure in coauthorship networks

  • 467 Accesses

  • 22 Citations


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.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. 1.

    Transitivity seems to be associated more commonly with directed networks (Wasserman and Faust 1994) than with undirected ones. Many network research papers and software packages implementing the Newman metric (2001b) still use transitivity to refer to triadic closure.

  2. 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. 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. 4.

    Although calculated against the same dataset, the clustering coefficient by the Newman (2001b) method in Opsahl (2013) is 0.3596, while the one in Newman (2001b) is 0.348.

  5. 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. 6.


  7. 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. 8.


  9. 9.


  10. 10.


  11. 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. 12.

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

  13. 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. 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. 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.


  1. Barabási AL, Jeong H, Neda Z, Ravasz E, Schubert A, Vicsek T (2002) Evolution of the social network of scientific collaborations. Phys A Stat Mech Appl 311(3–4):590–614. doi:10.1016/s0378-4371(02)00736-7

  2. Burt RS (2005) Brokerage and closure: an introduction to social capital. Oxford University Press, Oxford

  3. Çavuşoğlu A, Türker İ (2013) Scientific collaboration network of Turkey. Chaos, Solitons Fractals 57:9–18

  4. Csardi G, Nepusz T (2006) The igraph software package for complex network research. Inter J Complex Syst 1695. http://igraph.org

  5. Fegley BD, Torvik VI (2013) Has large-scale named-entity network analysis been resting on a flawed assumption? PLoS ONE 8(7):1–16. doi:10.1371/journal.pone.0070299

  6. Franceschet M (2011) Collaboration in computer science: a network science approach. J Am Soc Inf Sci Technol 62(10):1992–2012. doi:10.1002/asi.21614

  7. Grossman JW (2002) Patterns of collaboration in mathematical research. SIAM News 35(9):8–9

  8. Hâncean M-G, Perc M (2016) Homophily in coauthorship networks of East European sociologists. Sci Rep. doi:10.1038/srep36152

  9. Hâncean M-G, Perc M, Vlăsceanu L (2014) Fragmented romanian sociology: growth and structure of the collaboration network. PLoS ONE 9(11):e113271

  10. Holland PW, Leinhardt S (1970) Method for detecting structure in sociometric data. Am J Sociol 76(3):492. doi:10.1086/224954

  11. Kim J, Diesner J (2015) The effect of data pre-processing on understanding the evolution of collaboration networks. J Informetr 9(1):226–236. doi:10.1016/j.joi.2015.01.002

  12. Kim J, Diesner J (2016) Distortive effects of initial-based name disambiguation on measurements of large-scale coauthorship networks. J Assoc Inf Sci Technol 67(6):1446–1461. doi:10.1002/asi.23489

  13. Kim J, Tao L, Lee S-H, Diesner J (2016) Evolution and structure of scientific co-publishing network in Korea between 1948–2011. Scientometrics 107(1):27–41. doi:10.1007/s11192-016-1878-5

  14. Kossinets G, Watts DJ (2006) Empirical analysis of an evolving social network. Science 311(5757):88–90. doi:10.1126/science.1116869

  15. Liben-Nowell D, Kleinberg J (2007) The link-prediction problem for social networks. J Am Soc Inform Sci Technol 58(7):1019–1031. doi:10.1002/asi.20591

  16. Lind PG, Gonzalez MC, Herrmann HJ (2005) Cycles and clustering in bipartite networks. Phys Rev E 72(5):056127. doi:10.1103/PhysRevE.72.056127

  17. Martin T, Ball B, Karrer B, Newman MEJ (2013) Coauthorship and citation patterns in the Physical Review. Phys Rev E 88(1):012814-1–012814-9. doi:10.1103/PhysRevE.88.012814

  18. McPherson M, Smith-Lovin L, Cook JM (2001) Birds of a feather: homophily in social networks. Ann Rev Sociol 27:415–444. doi:10.1146/annurev.soc.27.1.415

  19. Moody J (2004) The structure of a social science collaboration network: disciplinary cohesion from 1963 to 1999. Am Sociol Rev 69(2):213–238

  20. Newman MEJ (2001a) Clustering and preferential attachment in growing networks. Phys Rev E. doi:10.1103/PhysRevE.64.025102

  21. Newman MEJ (2001b) The structure of scientific collaboration networks. Proc Natl Acad Sci USA 98(2):404–409. doi:10.1073/pnas.021544898

  22. Newman MEJ, Strogatz SH, Watts DJ (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E 64(2):026118

  23. Opsahl T (2009) Structure and evolution of weighted networks. University of London (Queen Mary College), London

  24. Opsahl T (2013) Triadic closure in two-mode networks: redefining the global and local clustering coefficients. Soc Netw 35(2):159–167

  25. Perc M (2010) Growth and structure of Slovenia’s scientific collaboration network. J Informetr 4(4):475–482

  26. Rapoport A (1953) Spread of information through a population with socio-structural bias: I. Assumption of transitivity. Bull Math Biophys 15(4):523–533

  27. Reitz F, Hoffmann O (2011) Did they notice? A case-study on the community contribution to data quality in DBLP. In: Gradmann S, Borri F, Meghini C, Schuldt H (eds) Research and advanced technology for digital libraries, TPDL 2011, vol 6966. Springer, Berlin, pp 204–215

  28. Robins G, Alexander M (2004) Small worlds among interlocking directors: network structure and distance in bipartite graphs. Comput Math Organ Theory 10(1):69–94. doi:10.1023/B:CMOT.0000032580.12184.c0

  29. Torvik VI, Smalheiser NR (2009) Author name disambiguation in MEDLINE. ACM Trans Knowl Discov Data 3(3):1–29. doi:10.1145/1552303.1552304

  30. Türker İ, Çavuşoğlu A (2016) Detailing the co-authorship networks in degree coupling, edge weight and academic age perspective. Chaos, Solitons Fractals 91:386–392

  31. Türker İ, Durgut R, Çavuşoğlu A (2016) Co-authorship network comparison of four Turkish universities. In: Paper presented at the international conference on research in education & science, Bodrum, Turkey

  32. Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, New York

  33. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’networks. Nature 393(6684):440–442

Download references


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.

Author information

Correspondence to Jinseok Kim.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation


  • Clustering coefficient
  • Transitivity
  • Triadic closure
  • Coauthorship networks