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Geodesic Cycle Length Distributions in Delusional and Other Social Networks

Authors
  • Stivala, Alex1
  • 1 Università della Svizzera italiana, Lugano , (Switzerland)
Type
Published Article
Journal
Journal of Social Structure
Publisher
Exeley Inc.
Publication Date
Jan 01, 2020
Volume
21
Issue
1
Pages
35–76
Identifiers
DOI: 10.21307/joss-2020-002
Source
Exeley
Keywords
License
Green

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.

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