A geodesic cycle in a graph is a cycle with no shortcuts, so that the shortest path between any two nodes in the cycle is the path along the cycle itself. A recently published paper used random graph models to investigate the geodesic cycle length distributions of a unique set of delusional social networks, first examined in an earlier work, as well as some other publicly available social networks. Here I test the hypothesis, suggested in the former work, that fictional character networks, and in particular those from works by a single author, might have geodesic cycle length distributions which are extremely unlikely under random graph models, as the delusional social networks do. The results do not show any support for this hypothesis. In addition, the recently published work is reproduced using a method for counting geodesic cycles exactly, rather than the approximate method used originally. The substantive conclusions of that work are unchanged, but some differences in the results for particular networks are described.

Keywords: Geodesic cycle, Isometric cycle, Exponential random graph model, ERGM, dk-series random graphs, Social networks, Fictional character networks

Code,  scripts and data

Code, scripts, and data are available on GitHub: https://github.com/stivalaa/geodesic_cycles. 

References

Martin, J. L. 2017. "The structure of node and edge generation in a delusional social network".  Journal of Social Structure, 18(1):1–22. doi.org/10.21307/joss-2018-005 

Martin, J. L. 2020. "Comment on Geodesic Cycle Length Distributions in Delusional and Other Social Networks". Journal of Social Structure 21(1):77-93. doi:10.21307/joss-2020-003 

Stivala, A. 2019. "The hollow ring of randomness: Large worlds in small data". Fourth Annual Australian Social Network Analysis Conference (ASNAC 2019), November 28-29, 2019, Adelaide, South Australia. https://stivalaa.github.io/AcademicWebsite/slides/geodesic_cycles_slides.pdf

Stivala, A. 2020 . "Geodesic cycle length distributions in delusional and other social networks". Journal of Social Structure 21(1):35-76. doi:10.21307/joss-2020-002 

Stivala, A. 2020. Reply to “Comment on Geodesic Cycle Length Distributions in Delusional and Other Social Networks”. Journal of Social Structure 21(1):94-106. doi:10.21307/joss-2020-004 

Stivala, A. 2023. "Geodesic cycle length distributions in fictional character networks". arXiv preprint arXiv:2303.11597