<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>dk</italic>-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.</p>
</abstract>

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.

Geodesic Cycle Length Distributions in Delusional and Other Social Networks

Journal of Social Structure

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Geodesic Cycle Length Distributions in Delusional and Other Social Networks"}

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...

Geodesic Cycle Length Distributions in Delusional and Other Social Networks

Article Category: research-article

Published Online: Oct 01, 2020

Page range: 35 - 76

DOI: https://doi.org/10.21307/joss-2020-002

Keywords
Geodesic cycle, Exponential random graph model, ERGM, -series random graphs, Social networks, Fictional networks, Dissociative identity disorder

© 2019 Alex Stivala; published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Geodesic Cycle Length Distributions in Delusional and Other Social Networks

Article Category: research-article

Published Online: Oct 01, 2020

Page range: 35 - 76

DOI: https://doi.org/10.21307/joss-2020-002

KeywordsGeodesic cycle, Exponential random graph model, ERGM, -series random graphs, Social networks, Fictional networks, Dissociative identity disorder

© 2019 Alex Stivala; published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Geodesic cycle, Exponential random graph model, ERGM, -series random graphs, Social networks, Fictional networks, Dissociative identity disorder