Code, scripts, and data for "Geodesic cycle length distributions in delusional and other social networks" (2020) and "Geodesic cycle length distributions in fictional character networks" (2023)
A recently published paper [Martin (2017) JoSS 18(1):1-21] investigates the structure of an unusual set of social networks, those of the alternate personalities described by a patient undergoing therapy for multiple personality disorder (now known as dissociative identity disorder). The structure of these networks is modeled using the dk-series, a sequence of nested network distributions of increasing complexity. Martin finds that the first of these networks contains a striking feature of a large "hollow ring"; a cycle with no shortcuts, so that the shortest path between any two nodes in the cycle is along the cycle (in more precise graph theory terms, this is a geodesic cycle). However the subsequent networks have much smaller largest cycles, smaller than those expected by the models. In this work I re-analyze these delusional social networks using exponential random graph models (ERGMs) and investigate the distribution of the lengths of geodesic cycles. I also conduct similar investigations for some other social networks, both fictional and empirical, and show that the geodesic cycle length distribution is a macro-level structure that can arise naturally from the micro-level processes modeled by the ERGM.
Keywords: Geodesic cycle, Exponential random graph model, ERGM, dk-series random graphs, Social networks, Fictional networks, Dissociative identity disorder
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
The code for finding "atomic cycles" uses the Waffles machine learning library https://github.com/mikegashler/waffles.
The code for counting geodesic cycles uses the CYPATH software from http://research.nii.ac.jp/~uno/code/cypath11.zip (see http://research.nii.ac.jp/~uno/code/cypath.html) to find chordless cycles.
Both the R and Python scripts use the igraph graph library https://igraph.org/.
Martin, J. L. 2017. "The structure of node and edge generation in a delusional social network". Journal of Social Structure, 18(1):1–22. https://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. https://doi.org/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. 2020a. "Geodesic cycle length distributions in delusional and other social networks". Journal of Social Structure, 21(1):35-76. https://doi.org/10.21307/joss-2020-002
Stivala, A. 2020b. "Reply to “Comment on Geodesic Cycle Length Distributions in Delusional and Other Social Networks”" Journal of Social Structure 21(1):94-106. https://doi.org/10.21307/joss-2020-004
Stivala, A. 2023. "Geodesic cycle length distributions in fictional character networks". arXiv preprint https://arxiv.org/abs/2303.11597