Bistability through triadic closure

Grindrod, P., Higham, D. J. and Parsons, M. C. (2012) Bistability through triadic closure. Internet Mathematics, 8 (4). pp. 402-423. doi: 10.1080/15427951.2012.714718

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/26937
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Centre for the Mathematics of Human Behaviour (CMOHB)
Uncontrolled Keywords	calibration, conjugacy, dynamic network, mean field theory, random graph, stochastic process, temporal network, triangulation, voice call data
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