A Hierarchy of Network Models Giving Bistability Under Triadic Closure

Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that triadic effect can lead bistability formation of large-scale social interaction networks. Here, depending on initial state and transient dynamics, system may evolve towards either two long-time states. In this work, we propose study a hierarchy network evolution models incorporate closure, building work Grindrod, Higham, Parsons [Internet Math., 8 (2012), pp. 402–423]. We use chemical kinetics framework, paying careful attention reaction rate scaling with respect size. macroscale regime, show rigorously bimodal steady distribution is admitted. This behavior corresponds existence distinct stable fixed points deterministic mean-field ODE. The model also seen capture an apparent metastability property microscale system. Computational simulations are used support analysis.