  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.
