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.
To link to this article DOI: 10.1080/15427951.2012.714718
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.