Coevolving nonlinear voter model with triadic closure

We study a nonlinear coevolving voter model with triadic closure local rewiring. We find three phases with different topological properties and configuration in the steady state: absorbing consensus phase with a single component, absorbing fragmented phase with two components in opposite consensus states, and a dynamically active shattered phase with many isolated nodes. This shattered phase, which does not exist for a coevolving model with global rewiring, has a lifetime that scale exponentially with system size. We characterize the transitions between these phases in terms of the size of the largest cluster, the number of clusters, and the magnetization. Our analysis provides a possible solution to reproduce isolated parts in adaptive networks and high clustering widely observed in social systems.