Bistability through triadic closure

Peter Grindrod, Desmond Higham, Mark C. Parsons

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We propose and analyse a class of evolving network models suitable for describing a dynamic topological structure. Applications include telecommunication, on-line social behaviour and information processing in neuroscience. We model the evolving network as a discrete time Markov chain, and study a very general framework where, conditioned on the current state, edges appear or disappear independently at the next timestep. We show how to exploit symmetries in the microscopic, localized rules in order to obtain conjugate classes of random graphs that simplify analysis and calibration of a model. Further, we develop a mean field theory for describing network evolution. For a simple but realistic scenario incorporating the triadic closure effect that has been empirically observed by social scientists (friends of friends tend to become friends), the mean field theory predicts bistable dynamics, and computational results confirm this prediction. We also discuss the calibration issue for a set of real cell phone data, and find support for a stratified model, where individuals are assigned to one of two distinct groups having different within-group and across-group dynamics
LanguageEnglish
Pages402-423
Number of pages22
JournalInternet Mathematics
Volume8
Issue number4
DOIs
Publication statusPublished - 2012

Fingerprint

Bistability
Closure
Mean-field Theory
Mean field theory
Calibration
Network Evolution
Social Behavior
Neuroscience
Topological Structure
Information Processing
Telecommunications
Random Graphs
Network Model
Computational Results
Markov chain
Simplify
Discrete-time
Model
Tend
Markov processes

Keywords

  • process
  • temporal network
  • triangulation
  • voice call data

Cite this

Grindrod, P., Higham, D., & Parsons, M. C. (2012). Bistability through triadic closure. Internet Mathematics, 8(4), 402-423. https://doi.org/10.1080/15427951.2012.714718
Grindrod, Peter ; Higham, Desmond ; Parsons, Mark C. / Bistability through triadic closure. In: Internet Mathematics. 2012 ; Vol. 8, No. 4. pp. 402-423.
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Grindrod, P, Higham, D & Parsons, MC 2012, 'Bistability through triadic closure' Internet Mathematics, vol. 8, no. 4, pp. 402-423. https://doi.org/10.1080/15427951.2012.714718

Bistability through triadic closure. / Grindrod, Peter; Higham, Desmond; Parsons, Mark C.

In: Internet Mathematics, Vol. 8, No. 4, 2012, p. 402-423.

Research output: Contribution to journalArticle

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